analysis.complex.basic ⟷ Mathlib.Analysis.Complex.Basic

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

@@ -5,7 +5,7 @@ Authors: Sébastien Gouëzel
 -/
 import Data.Complex.Module
 import Data.Complex.Exponential
-import Data.IsROrC.Basic
+import Analysis.RCLike.Basic
 import Topology.Algebra.InfiniteSum.Module
 import Topology.Instances.RealVectorSpace
 
@@ -210,7 +210,7 @@ theorem norm_nat (n : ℕ) : ‖(n : ℂ)‖ = n :=
 #print Complex.norm_int /-
 @[simp]
 theorem norm_int {n : ℤ} : ‖(n : ℂ)‖ = |n| := by
-  simp (config := { singlePass := true }) [← Rat.cast_coe_int]
+  simp (config := { singlePass := true }) [← Rat.cast_intCast]
 #align complex.norm_int Complex.norm_int
 -/
 
@@ -550,7 +550,7 @@ theorem ofRealCLM_apply (x : ℝ) : ofRealCLM x = x :=
 #align complex.of_real_clm_apply Complex.ofRealCLM_apply
 -/
 
-noncomputable instance : IsROrC ℂ
+noncomputable instance : RCLike ℂ
     where
   re := ⟨Complex.re, Complex.zero_re, Complex.add_re⟩
   im := ⟨Complex.im, Complex.zero_im, Complex.add_im⟩
@@ -576,16 +576,16 @@ noncomputable instance : IsROrC ℂ
       Complex.norm_eq_abs]
   hMul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.I_im]
 
-#print IsROrC.re_eq_complex_re /-
-theorem IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
+#print RCLike.re_eq_complex_re /-
+theorem RCLike.re_eq_complex_re : ⇑(RCLike.re : ℂ →+ ℝ) = Complex.re :=
   rfl
-#align is_R_or_C.re_eq_complex_re IsROrC.re_eq_complex_re
+#align is_R_or_C.re_eq_complex_re RCLike.re_eq_complex_re
 -/
 
-#print IsROrC.im_eq_complex_im /-
-theorem IsROrC.im_eq_complex_im : ⇑(IsROrC.im : ℂ →+ ℝ) = Complex.im :=
+#print RCLike.im_eq_complex_im /-
+theorem RCLike.im_eq_complex_im : ⇑(RCLike.im : ℂ →+ ℝ) = Complex.im :=
   rfl
-#align is_R_or_C.im_eq_complex_im IsROrC.im_eq_complex_im
+#align is_R_or_C.im_eq_complex_im RCLike.im_eq_complex_im
 -/
 
 section ComplexOrder
@@ -594,7 +594,7 @@ open scoped ComplexOrder
 
 #print Complex.eq_coe_norm_of_nonneg /-
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
-  rw [eq_re_of_real_le hz, IsROrC.norm_ofReal, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
+  rw [eq_re_of_real_le hz, RCLike.norm_ofReal, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
 -/
 
@@ -602,97 +602,97 @@ end ComplexOrder
 
 end Complex
 
-namespace IsROrC
+namespace RCLike
 
 open scoped ComplexConjugate
 
-local notation "reC" => @IsROrC.re ℂ _
+local notation "reC" => @RCLike.re ℂ _
 
-local notation "imC" => @IsROrC.im ℂ _
+local notation "imC" => @RCLike.im ℂ _
 
-local notation "IC" => @IsROrC.i ℂ _
+local notation "IC" => @RCLike.i ℂ _
 
-local notation "norm_sqC" => @IsROrC.normSq ℂ _
+local notation "norm_sqC" => @RCLike.normSq ℂ _
 
-#print IsROrC.re_to_complex /-
+#print RCLike.re_to_complex /-
 @[simp]
 theorem re_to_complex {x : ℂ} : reC x = x.re :=
   rfl
-#align is_R_or_C.re_to_complex IsROrC.re_to_complex
+#align is_R_or_C.re_to_complex RCLike.re_to_complex
 -/
 
-#print IsROrC.im_to_complex /-
+#print RCLike.im_to_complex /-
 @[simp]
 theorem im_to_complex {x : ℂ} : imC x = x.im :=
   rfl
-#align is_R_or_C.im_to_complex IsROrC.im_to_complex
+#align is_R_or_C.im_to_complex RCLike.im_to_complex
 -/
 
-#print IsROrC.I_to_complex /-
+#print RCLike.I_to_complex /-
 @[simp]
 theorem I_to_complex : IC = Complex.I :=
   rfl
-#align is_R_or_C.I_to_complex IsROrC.I_to_complex
+#align is_R_or_C.I_to_complex RCLike.I_to_complex
 -/
 
-#print IsROrC.normSq_to_complex /-
+#print RCLike.normSq_to_complex /-
 @[simp]
 theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x :=
   rfl
-#align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complex
+#align is_R_or_C.norm_sq_to_complex RCLike.normSq_to_complex
 -/
 
 section tsum
 
-variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]
+variable {α : Type _} (𝕜 : Type _) [RCLike 𝕜]
 
-#print IsROrC.hasSum_conj /-
+#print RCLike.hasSum_conj /-
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
   conjCLE.HasSum
-#align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
+#align is_R_or_C.has_sum_conj RCLike.hasSum_conj
 -/
 
-#print IsROrC.hasSum_conj' /-
+#print RCLike.hasSum_conj' /-
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   conjCLE.hasSum'
-#align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
+#align is_R_or_C.has_sum_conj' RCLike.hasSum_conj'
 -/
 
-#print IsROrC.summable_conj /-
+#print RCLike.summable_conj /-
 @[simp]
 theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Summable f :=
   summable_star_iff
-#align is_R_or_C.summable_conj IsROrC.summable_conj
+#align is_R_or_C.summable_conj RCLike.summable_conj
 -/
 
 variable {𝕜}
 
-#print IsROrC.conj_tsum /-
+#print RCLike.conj_tsum /-
 theorem conj_tsum (f : α → 𝕜) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   tsum_star
-#align is_R_or_C.conj_tsum IsROrC.conj_tsum
+#align is_R_or_C.conj_tsum RCLike.conj_tsum
 -/
 
 variable (𝕜)
 
-#print IsROrC.hasSum_ofReal /-
+#print RCLike.hasSum_ofReal /-
 @[simp, norm_cast]
 theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : 𝕜)) x ↔ HasSum f x :=
-  ⟨fun h => by simpa only [IsROrC.reCLM_apply, IsROrC.ofReal_re] using re_clm.has_sum h,
+  ⟨fun h => by simpa only [RCLike.reCLM_apply, RCLike.ofReal_re] using re_clm.has_sum h,
     ofRealCLM.HasSum⟩
-#align is_R_or_C.has_sum_of_real IsROrC.hasSum_ofReal
+#align is_R_or_C.has_sum_of_real RCLike.hasSum_ofReal
 -/
 
-#print IsROrC.summable_ofReal /-
+#print RCLike.summable_ofReal /-
 @[simp, norm_cast]
 theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : 𝕜)) ↔ Summable f :=
-  ⟨fun h => by simpa only [IsROrC.reCLM_apply, IsROrC.ofReal_re] using re_clm.summable h,
+  ⟨fun h => by simpa only [RCLike.reCLM_apply, RCLike.ofReal_re] using re_clm.summable h,
     ofRealCLM.Summable⟩
-#align is_R_or_C.summable_of_real IsROrC.summable_ofReal
+#align is_R_or_C.summable_of_real RCLike.summable_ofReal
 -/
 
-#print IsROrC.ofReal_tsum /-
+#print RCLike.ofReal_tsum /-
 @[norm_cast]
 theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, f a :=
   by
@@ -701,50 +701,50 @@ theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, f a :
   ·
     rw [tsum_eq_zero_of_not_summable h,
       tsum_eq_zero_of_not_summable ((summable_of_real _).Not.mpr h), of_real_zero]
-#align is_R_or_C.of_real_tsum IsROrC.ofReal_tsum
+#align is_R_or_C.of_real_tsum RCLike.ofReal_tsum
 -/
 
-#print IsROrC.hasSum_re /-
+#print RCLike.hasSum_re /-
 theorem hasSum_re {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => re (f x)) (re x) :=
   reCLM.HasSum h
-#align is_R_or_C.has_sum_re IsROrC.hasSum_re
+#align is_R_or_C.has_sum_re RCLike.hasSum_re
 -/
 
-#print IsROrC.hasSum_im /-
+#print RCLike.hasSum_im /-
 theorem hasSum_im {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => im (f x)) (im x) :=
   imCLM.HasSum h
-#align is_R_or_C.has_sum_im IsROrC.hasSum_im
+#align is_R_or_C.has_sum_im RCLike.hasSum_im
 -/
 
-#print IsROrC.re_tsum /-
+#print RCLike.re_tsum /-
 theorem re_tsum {f : α → 𝕜} (h : Summable f) : re (∑' a, f a) = ∑' a, re (f a) :=
   reCLM.map_tsum h
-#align is_R_or_C.re_tsum IsROrC.re_tsum
+#align is_R_or_C.re_tsum RCLike.re_tsum
 -/
 
-#print IsROrC.im_tsum /-
+#print RCLike.im_tsum /-
 theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a, im (f a) :=
   imCLM.map_tsum h
-#align is_R_or_C.im_tsum IsROrC.im_tsum
+#align is_R_or_C.im_tsum RCLike.im_tsum
 -/
 
 variable {𝕜}
 
-#print IsROrC.hasSum_iff /-
+#print RCLike.hasSum_iff /-
 theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
     HasSum f c ↔ HasSum (fun x => re (f x)) (re c) ∧ HasSum (fun x => im (f x)) (im c) :=
   by
   refine' ⟨fun h => ⟨has_sum_re _ h, has_sum_im _ h⟩, _⟩
   rintro ⟨h₁, h₂⟩
-  rw [← IsROrC.re_add_im c]
+  rw [← RCLike.re_add_im c]
   convert ((has_sum_of_real 𝕜).mpr h₁).add (((has_sum_of_real 𝕜).mpr h₂).hMul_right I)
-  simp_rw [IsROrC.re_add_im]
-#align is_R_or_C.has_sum_iff IsROrC.hasSum_iff
+  simp_rw [RCLike.re_add_im]
+#align is_R_or_C.has_sum_iff RCLike.hasSum_iff
 -/
 
 end tsum
 
-end IsROrC
+end RCLike
 
 namespace Complex
 
@@ -766,78 +766,78 @@ open scoped ComplexConjugate
 #print Complex.hasSum_conj /-
 @[simp]
 theorem hasSum_conj {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
-  IsROrC.hasSum_conj _
+  RCLike.hasSum_conj _
 #align complex.has_sum_conj Complex.hasSum_conj
 -/
 
 #print Complex.hasSum_conj' /-
 theorem hasSum_conj' {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
-  IsROrC.hasSum_conj' _
+  RCLike.hasSum_conj' _
 #align complex.has_sum_conj' Complex.hasSum_conj'
 -/
 
 #print Complex.summable_conj /-
 @[simp]
 theorem summable_conj {f : α → ℂ} : (Summable fun x => conj (f x)) ↔ Summable f :=
-  IsROrC.summable_conj _
+  RCLike.summable_conj _
 #align complex.summable_conj Complex.summable_conj
 -/
 
 #print Complex.conj_tsum /-
 theorem conj_tsum (f : α → ℂ) : conj (∑' a, f a) = ∑' a, conj (f a) :=
-  IsROrC.conj_tsum _
+  RCLike.conj_tsum _
 #align complex.conj_tsum Complex.conj_tsum
 -/
 
 #print Complex.hasSum_ofReal /-
 @[simp, norm_cast]
 theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : ℂ)) x ↔ HasSum f x :=
-  IsROrC.hasSum_ofReal _
+  RCLike.hasSum_ofReal _
 #align complex.has_sum_of_real Complex.hasSum_ofReal
 -/
 
 #print Complex.summable_ofReal /-
 @[simp, norm_cast]
 theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : ℂ)) ↔ Summable f :=
-  IsROrC.summable_ofReal _
+  RCLike.summable_ofReal _
 #align complex.summable_of_real Complex.summable_ofReal
 -/
 
 #print Complex.ofReal_tsum /-
 @[norm_cast]
 theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : ℂ) = ∑' a, f a :=
-  IsROrC.ofReal_tsum _ _
+  RCLike.ofReal_tsum _ _
 #align complex.of_real_tsum Complex.ofReal_tsum
 -/
 
 #print Complex.hasSum_re /-
 theorem hasSum_re {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).re) x.re :=
-  IsROrC.hasSum_re _ h
+  RCLike.hasSum_re _ h
 #align complex.has_sum_re Complex.hasSum_re
 -/
 
 #print Complex.hasSum_im /-
 theorem hasSum_im {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).im) x.im :=
-  IsROrC.hasSum_im _ h
+  RCLike.hasSum_im _ h
 #align complex.has_sum_im Complex.hasSum_im
 -/
 
 #print Complex.re_tsum /-
 theorem re_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).re = ∑' a, (f a).re :=
-  IsROrC.re_tsum _ h
+  RCLike.re_tsum _ h
 #align complex.re_tsum Complex.re_tsum
 -/
 
 #print Complex.im_tsum /-
 theorem im_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).im = ∑' a, (f a).im :=
-  IsROrC.im_tsum _ h
+  RCLike.im_tsum _ h
 #align complex.im_tsum Complex.im_tsum
 -/
 
 #print Complex.hasSum_iff /-
 theorem hasSum_iff (f : α → ℂ) (c : ℂ) :
     HasSum f c ↔ HasSum (fun x => (f x).re) c.re ∧ HasSum (fun x => (f x).im) c.im :=
-  IsROrC.hasSum_iff _ _
+  RCLike.hasSum_iff _ _
 #align complex.has_sum_iff Complex.hasSum_iff
 -/
 

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

@@ -301,17 +301,17 @@ theorem uniformEmbedding_equivRealProd : UniformEmbedding equivRealProd :=
 instance : CompleteSpace ℂ :=
   (completeSpace_congr uniformEmbedding_equivRealProd).mpr inferInstance
 
-#print Complex.equivRealProdClm /-
+#print Complex.equivRealProdCLM /-
 /-- The natural `continuous_linear_equiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
-def equivRealProdClm : ℂ ≃L[ℝ] ℝ × ℝ :=
+def equivRealProdCLM : ℂ ≃L[ℝ] ℝ × ℝ :=
   equivRealProdLm.toContinuousLinearEquivOfBounds 1 (Real.sqrt 2) equivRealProd_apply_le' fun p =>
     abs_le_sqrt_two_mul_max (equivRealProd.symm p)
-#align complex.equiv_real_prod_clm Complex.equivRealProdClm
+#align complex.equiv_real_prod_clm Complex.equivRealProdCLM
 -/
 
 instance : ProperSpace ℂ :=
-  (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdClm.toHomeomorph).ProperSpace
+  (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdCLM.toHomeomorph).ProperSpace
 
 #print Complex.tendsto_abs_cocompact_atTop /-
 /-- The `abs` function on `ℂ` is proper. -/
@@ -331,66 +331,66 @@ theorem tendsto_normSq_cocompact_atTop : Filter.Tendsto normSq (Filter.cocompact
 
 open ContinuousLinearMap
 
-#print Complex.reClm /-
+#print Complex.reCLM /-
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
-def reClm : ℂ →L[ℝ] ℝ :=
+def reCLM : ℂ →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by simp [abs_re_le_abs]
-#align complex.re_clm Complex.reClm
+#align complex.re_clm Complex.reCLM
 -/
 
 #print Complex.continuous_re /-
 @[continuity]
 theorem continuous_re : Continuous re :=
-  reClm.Continuous
+  reCLM.Continuous
 #align complex.continuous_re Complex.continuous_re
 -/
 
-#print Complex.reClm_coe /-
+#print Complex.reCLM_coe /-
 @[simp]
-theorem reClm_coe : (coe reClm : ℂ →ₗ[ℝ] ℝ) = reLm :=
+theorem reCLM_coe : (coe reCLM : ℂ →ₗ[ℝ] ℝ) = reLm :=
   rfl
-#align complex.re_clm_coe Complex.reClm_coe
+#align complex.re_clm_coe Complex.reCLM_coe
 -/
 
-#print Complex.reClm_apply /-
+#print Complex.reCLM_apply /-
 @[simp]
-theorem reClm_apply (z : ℂ) : (reClm : ℂ → ℝ) z = z.re :=
+theorem reCLM_apply (z : ℂ) : (reCLM : ℂ → ℝ) z = z.re :=
   rfl
-#align complex.re_clm_apply Complex.reClm_apply
+#align complex.re_clm_apply Complex.reCLM_apply
 -/
 
-#print Complex.imClm /-
+#print Complex.imCLM /-
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
-def imClm : ℂ →L[ℝ] ℝ :=
+def imCLM : ℂ →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by simp [abs_im_le_abs]
-#align complex.im_clm Complex.imClm
+#align complex.im_clm Complex.imCLM
 -/
 
 #print Complex.continuous_im /-
 @[continuity]
 theorem continuous_im : Continuous im :=
-  imClm.Continuous
+  imCLM.Continuous
 #align complex.continuous_im Complex.continuous_im
 -/
 
-#print Complex.imClm_coe /-
+#print Complex.imCLM_coe /-
 @[simp]
-theorem imClm_coe : (coe imClm : ℂ →ₗ[ℝ] ℝ) = imLm :=
+theorem imCLM_coe : (coe imCLM : ℂ →ₗ[ℝ] ℝ) = imLm :=
   rfl
-#align complex.im_clm_coe Complex.imClm_coe
+#align complex.im_clm_coe Complex.imCLM_coe
 -/
 
-#print Complex.imClm_apply /-
+#print Complex.imCLM_apply /-
 @[simp]
-theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
+theorem imCLM_apply (z : ℂ) : (imCLM : ℂ → ℝ) z = z.im :=
   rfl
-#align complex.im_clm_apply Complex.imClm_apply
+#align complex.im_clm_apply Complex.imCLM_apply
 -/
 
 #print Complex.restrictScalars_one_smulRight' /-
 theorem restrictScalars_one_smulRight' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =
-      reClm.smul_right x + I • imClm.smul_right x :=
+      reCLM.smul_right x + I • imCLM.smul_right x :=
   by ext ⟨a, b⟩; simp [mk_eq_add_mul_I, add_smul, mul_smul, smul_comm I]
 #align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'
 -/
@@ -402,30 +402,30 @@ theorem restrictScalars_one_smulRight (x : ℂ) :
 #align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRight
 -/
 
-#print Complex.conjLie /-
+#print Complex.conjLIE /-
 /-- The complex-conjugation function from `ℂ` to itself is an isometric linear equivalence. -/
-def conjLie : ℂ ≃ₗᵢ[ℝ] ℂ :=
+def conjLIE : ℂ ≃ₗᵢ[ℝ] ℂ :=
   ⟨conjAe.toLinearEquiv, abs_conj⟩
-#align complex.conj_lie Complex.conjLie
+#align complex.conj_lie Complex.conjLIE
 -/
 
-#print Complex.conjLie_apply /-
+#print Complex.conjLIE_apply /-
 @[simp]
-theorem conjLie_apply (z : ℂ) : conjLie z = conj z :=
+theorem conjLIE_apply (z : ℂ) : conjLIE z = conj z :=
   rfl
-#align complex.conj_lie_apply Complex.conjLie_apply
+#align complex.conj_lie_apply Complex.conjLIE_apply
 -/
 
-#print Complex.conjLie_symm /-
+#print Complex.conjLIE_symm /-
 @[simp]
-theorem conjLie_symm : conjLie.symm = conjLie :=
+theorem conjLIE_symm : conjLIE.symm = conjLIE :=
   rfl
-#align complex.conj_lie_symm Complex.conjLie_symm
+#align complex.conj_lie_symm Complex.conjLIE_symm
 -/
 
 #print Complex.isometry_conj /-
 theorem isometry_conj : Isometry (conj : ℂ → ℂ) :=
-  conjLie.Isometry
+  conjLIE.Isometry
 #align complex.isometry_conj Complex.isometry_conj
 -/
 
@@ -456,7 +456,7 @@ theorem nndist_conj_comm (z w : ℂ) : nndist (conj z) w = nndist z (conj w) :=
 -/
 
 instance : ContinuousStar ℂ :=
-  ⟨conjLie.Continuous⟩
+  ⟨conjLIE.Continuous⟩
 
 #print Complex.continuous_conj /-
 @[continuity]
@@ -477,44 +477,44 @@ theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous
 #align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuous
 -/
 
-#print Complex.conjCle /-
+#print Complex.conjCLE /-
 /-- Continuous linear equiv version of the conj function, from `ℂ` to `ℂ`. -/
-def conjCle : ℂ ≃L[ℝ] ℂ :=
-  conjLie
-#align complex.conj_cle Complex.conjCle
+def conjCLE : ℂ ≃L[ℝ] ℂ :=
+  conjLIE
+#align complex.conj_cle Complex.conjCLE
 -/
 
-#print Complex.conjCle_coe /-
+#print Complex.conjCLE_coe /-
 @[simp]
-theorem conjCle_coe : conjCle.toLinearEquiv = conjAe.toLinearEquiv :=
+theorem conjCLE_coe : conjCLE.toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
-#align complex.conj_cle_coe Complex.conjCle_coe
+#align complex.conj_cle_coe Complex.conjCLE_coe
 -/
 
-#print Complex.conjCle_apply /-
+#print Complex.conjCLE_apply /-
 @[simp]
-theorem conjCle_apply (z : ℂ) : conjCle z = conj z :=
+theorem conjCLE_apply (z : ℂ) : conjCLE z = conj z :=
   rfl
-#align complex.conj_cle_apply Complex.conjCle_apply
+#align complex.conj_cle_apply Complex.conjCLE_apply
 -/
 
-#print Complex.ofRealLi /-
+#print Complex.ofRealLI /-
 /-- Linear isometry version of the canonical embedding of `ℝ` in `ℂ`. -/
-def ofRealLi : ℝ →ₗᵢ[ℝ] ℂ :=
+def ofRealLI : ℝ →ₗᵢ[ℝ] ℂ :=
   ⟨ofRealAm.toLinearMap, norm_real⟩
-#align complex.of_real_li Complex.ofRealLi
+#align complex.of_real_li Complex.ofRealLI
 -/
 
 #print Complex.isometry_ofReal /-
 theorem isometry_ofReal : Isometry (coe : ℝ → ℂ) :=
-  ofRealLi.Isometry
+  ofRealLI.Isometry
 #align complex.isometry_of_real Complex.isometry_ofReal
 -/
 
 #print Complex.continuous_ofReal /-
 @[continuity]
 theorem continuous_ofReal : Continuous (coe : ℝ → ℂ) :=
-  ofRealLi.Continuous
+  ofRealLI.Continuous
 #align complex.continuous_of_real Complex.continuous_ofReal
 -/
 
@@ -529,25 +529,25 @@ theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) :
 #align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuous
 -/
 
-#print Complex.ofRealClm /-
+#print Complex.ofRealCLM /-
 /-- Continuous linear map version of the canonical embedding of `ℝ` in `ℂ`. -/
-def ofRealClm : ℝ →L[ℝ] ℂ :=
-  ofRealLi.toContinuousLinearMap
-#align complex.of_real_clm Complex.ofRealClm
+def ofRealCLM : ℝ →L[ℝ] ℂ :=
+  ofRealLI.toContinuousLinearMap
+#align complex.of_real_clm Complex.ofRealCLM
 -/
 
-#print Complex.ofRealClm_coe /-
+#print Complex.ofRealCLM_coe /-
 @[simp]
-theorem ofRealClm_coe : (ofRealClm : ℝ →ₗ[ℝ] ℂ) = ofRealAm.toLinearMap :=
+theorem ofRealCLM_coe : (ofRealCLM : ℝ →ₗ[ℝ] ℂ) = ofRealAm.toLinearMap :=
   rfl
-#align complex.of_real_clm_coe Complex.ofRealClm_coe
+#align complex.of_real_clm_coe Complex.ofRealCLM_coe
 -/
 
-#print Complex.ofRealClm_apply /-
+#print Complex.ofRealCLM_apply /-
 @[simp]
-theorem ofRealClm_apply (x : ℝ) : ofRealClm x = x :=
+theorem ofRealCLM_apply (x : ℝ) : ofRealCLM x = x :=
   rfl
-#align complex.of_real_clm_apply Complex.ofRealClm_apply
+#align complex.of_real_clm_apply Complex.ofRealCLM_apply
 -/
 
 noncomputable instance : IsROrC ℂ
@@ -649,13 +649,13 @@ variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]
 #print IsROrC.hasSum_conj /-
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
-  conjCle.HasSum
+  conjCLE.HasSum
 #align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
 -/
 
 #print IsROrC.hasSum_conj' /-
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
-  conjCle.hasSum'
+  conjCLE.hasSum'
 #align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
 -/
 
@@ -679,16 +679,16 @@ variable (𝕜)
 #print IsROrC.hasSum_ofReal /-
 @[simp, norm_cast]
 theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : 𝕜)) x ↔ HasSum f x :=
-  ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using re_clm.has_sum h,
-    ofRealClm.HasSum⟩
+  ⟨fun h => by simpa only [IsROrC.reCLM_apply, IsROrC.ofReal_re] using re_clm.has_sum h,
+    ofRealCLM.HasSum⟩
 #align is_R_or_C.has_sum_of_real IsROrC.hasSum_ofReal
 -/
 
 #print IsROrC.summable_ofReal /-
 @[simp, norm_cast]
 theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : 𝕜)) ↔ Summable f :=
-  ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using re_clm.summable h,
-    ofRealClm.Summable⟩
+  ⟨fun h => by simpa only [IsROrC.reCLM_apply, IsROrC.ofReal_re] using re_clm.summable h,
+    ofRealCLM.Summable⟩
 #align is_R_or_C.summable_of_real IsROrC.summable_ofReal
 -/
 
@@ -706,25 +706,25 @@ theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, f a :
 
 #print IsROrC.hasSum_re /-
 theorem hasSum_re {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => re (f x)) (re x) :=
-  reClm.HasSum h
+  reCLM.HasSum h
 #align is_R_or_C.has_sum_re IsROrC.hasSum_re
 -/
 
 #print IsROrC.hasSum_im /-
 theorem hasSum_im {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => im (f x)) (im x) :=
-  imClm.HasSum h
+  imCLM.HasSum h
 #align is_R_or_C.has_sum_im IsROrC.hasSum_im
 -/
 
 #print IsROrC.re_tsum /-
 theorem re_tsum {f : α → 𝕜} (h : Summable f) : re (∑' a, f a) = ∑' a, re (f a) :=
-  reClm.map_tsum h
+  reCLM.map_tsum h
 #align is_R_or_C.re_tsum IsROrC.re_tsum
 -/
 
 #print IsROrC.im_tsum /-
 theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a, im (f a) :=
-  imClm.map_tsum h
+  imCLM.map_tsum h
 #align is_R_or_C.im_tsum IsROrC.im_tsum
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3365b20c2ffa7c35e47e5209b89ba9abdddf3ffe

@@ -203,7 +203,7 @@ theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| := by rw [← of_real
 #print Complex.norm_nat /-
 @[simp]
 theorem norm_nat (n : ℕ) : ‖(n : ℂ)‖ = n :=
-  abs_of_nat _
+  abs_natCast _
 #align complex.norm_nat Complex.norm_nat
 -/
 

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

@@ -3,11 +3,11 @@ Copyright (c) Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Data.Complex.Module
-import Mathbin.Data.Complex.Exponential
-import Mathbin.Data.IsROrC.Basic
-import Mathbin.Topology.Algebra.InfiniteSum.Module
-import Mathbin.Topology.Instances.RealVectorSpace
+import Data.Complex.Module
+import Data.Complex.Exponential
+import Data.IsROrC.Basic
+import Topology.Algebra.InfiniteSum.Module
+import Topology.Instances.RealVectorSpace
 
 #align_import analysis.complex.basic from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
 

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

@@ -556,7 +556,7 @@ noncomputable instance : IsROrC ℂ
   im := ⟨Complex.im, Complex.zero_im, Complex.add_im⟩
   I := Complex.I
   i_re_ax := by simp only [AddMonoidHom.coe_mk, Complex.I_re]
-  i_mul_i_ax := by simp only [Complex.I_mul_I, eq_self_iff_true, or_true_iff]
+  i_hMul_i_ax := by simp only [Complex.I_mul_I, eq_self_iff_true, or_true_iff]
   re_add_im_ax z := by
     simp only [AddMonoidHom.coe_mk, Complex.re_add_im, Complex.coe_algebraMap,
       Complex.ofReal_eq_coe]
@@ -566,15 +566,15 @@ noncomputable instance : IsROrC ℂ
   of_real_im_ax r := by
     simp only [AddMonoidHom.coe_mk, Complex.ofReal_im, Complex.coe_algebraMap,
       Complex.ofReal_eq_coe]
-  mul_re_ax z w := by simp only [Complex.mul_re, AddMonoidHom.coe_mk]
-  mul_im_ax z w := by simp only [AddMonoidHom.coe_mk, Complex.mul_im]
+  hMul_re_ax z w := by simp only [Complex.mul_re, AddMonoidHom.coe_mk]
+  hMul_im_ax z w := by simp only [AddMonoidHom.coe_mk, Complex.mul_im]
   conj_re_ax z := rfl
   conj_im_ax z := rfl
   conj_i_ax := by simp only [Complex.conj_I, RingHom.coe_mk]
   norm_sq_eq_def_ax z := by
     simp only [← Complex.normSq_eq_abs, ← Complex.normSq_apply, AddMonoidHom.coe_mk,
       Complex.norm_eq_abs]
-  mul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.I_im]
+  hMul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.I_im]
 
 #print IsROrC.re_eq_complex_re /-
 theorem IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
@@ -737,7 +737,7 @@ theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
   refine' ⟨fun h => ⟨has_sum_re _ h, has_sum_im _ h⟩, _⟩
   rintro ⟨h₁, h₂⟩
   rw [← IsROrC.re_add_im c]
-  convert ((has_sum_of_real 𝕜).mpr h₁).add (((has_sum_of_real 𝕜).mpr h₂).mul_right I)
+  convert ((has_sum_of_real 𝕜).mpr h₁).add (((has_sum_of_real 𝕜).mpr h₂).hMul_right I)
   simp_rw [IsROrC.re_add_im]
 #align is_R_or_C.has_sum_iff IsROrC.hasSum_iff
 -/

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

@@ -2,11 +2,6 @@
 Copyright (c) Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module analysis.complex.basic
-! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Complex.Module
 import Mathbin.Data.Complex.Exponential
@@ -14,6 +9,8 @@ import Mathbin.Data.IsROrC.Basic
 import Mathbin.Topology.Algebra.InfiniteSum.Module
 import Mathbin.Topology.Instances.RealVectorSpace
 
+#align_import analysis.complex.basic from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
+
 /-!
 # Normed space structure on `ℂ`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -73,7 +73,7 @@ instance : NormedAddCommGroup ℂ :=
       eq_zero_of_map_eq_zero' := fun _ => abs.eq_zero.1 }
 
 instance : NormedField ℂ :=
-  { Complex.field,
+  { Complex.instField,
     Complex.normedAddCommGroup with
     norm := abs
     dist_eq := fun _ _ => rfl

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

@@ -52,14 +52,18 @@ open scoped ComplexConjugate Topology
 instance : Norm ℂ :=
   ⟨abs⟩
 
+#print Complex.norm_eq_abs /-
 @[simp]
 theorem norm_eq_abs (z : ℂ) : ‖z‖ = abs z :=
   rfl
 #align complex.norm_eq_abs Complex.norm_eq_abs
+-/
 
+#print Complex.norm_exp_ofReal_mul_I /-
 theorem norm_exp_ofReal_mul_I (t : ℝ) : ‖exp (t * I)‖ = 1 := by
   simp only [norm_eq_abs, abs_exp_of_real_mul_I]
 #align complex.norm_exp_of_real_mul_I Complex.norm_exp_ofReal_mul_I
+-/
 
 instance : NormedAddCommGroup ℂ :=
   AddGroupNorm.toNormedAddCommGroup
@@ -92,134 +96,192 @@ instance {R : Type _} [NormedField R] [NormedAlgebra R ℝ] : NormedAlgebra R 
 
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
+#print NormedSpace.complexToReal /-
 -- see Note [lower instance priority]
 /-- The module structure from `module.complex_to_real` is a normed space. -/
 instance (priority := 900) NormedSpace.complexToReal : NormedSpace ℝ E :=
   NormedSpace.restrictScalars ℝ ℂ E
 #align normed_space.complex_to_real NormedSpace.complexToReal
+-/
 
+#print Complex.dist_eq /-
 theorem dist_eq (z w : ℂ) : dist z w = abs (z - w) :=
   rfl
 #align complex.dist_eq Complex.dist_eq
+-/
 
+#print Complex.dist_eq_re_im /-
 theorem dist_eq_re_im (z w : ℂ) : dist z w = Real.sqrt ((z.re - w.re) ^ 2 + (z.im - w.im) ^ 2) := by
   rw [sq, sq]; rfl
 #align complex.dist_eq_re_im Complex.dist_eq_re_im
+-/
 
+#print Complex.dist_mk /-
 @[simp]
 theorem dist_mk (x₁ y₁ x₂ y₂ : ℝ) :
     dist (mk x₁ y₁) (mk x₂ y₂) = Real.sqrt ((x₁ - x₂) ^ 2 + (y₁ - y₂) ^ 2) :=
   dist_eq_re_im _ _
 #align complex.dist_mk Complex.dist_mk
+-/
 
+#print Complex.dist_of_re_eq /-
 theorem dist_of_re_eq {z w : ℂ} (h : z.re = w.re) : dist z w = dist z.im w.im := by
   rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, zero_add, Real.sqrt_sq_eq_abs, Real.dist_eq]
 #align complex.dist_of_re_eq Complex.dist_of_re_eq
+-/
 
+#print Complex.nndist_of_re_eq /-
 theorem nndist_of_re_eq {z w : ℂ} (h : z.re = w.re) : nndist z w = nndist z.im w.im :=
   NNReal.eq <| dist_of_re_eq h
 #align complex.nndist_of_re_eq Complex.nndist_of_re_eq
+-/
 
+#print Complex.edist_of_re_eq /-
 theorem edist_of_re_eq {z w : ℂ} (h : z.re = w.re) : edist z w = edist z.im w.im := by
   rw [edist_nndist, edist_nndist, nndist_of_re_eq h]
 #align complex.edist_of_re_eq Complex.edist_of_re_eq
+-/
 
+#print Complex.dist_of_im_eq /-
 theorem dist_of_im_eq {z w : ℂ} (h : z.im = w.im) : dist z w = dist z.re w.re := by
   rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, add_zero, Real.sqrt_sq_eq_abs, Real.dist_eq]
 #align complex.dist_of_im_eq Complex.dist_of_im_eq
+-/
 
+#print Complex.nndist_of_im_eq /-
 theorem nndist_of_im_eq {z w : ℂ} (h : z.im = w.im) : nndist z w = nndist z.re w.re :=
   NNReal.eq <| dist_of_im_eq h
 #align complex.nndist_of_im_eq Complex.nndist_of_im_eq
+-/
 
+#print Complex.edist_of_im_eq /-
 theorem edist_of_im_eq {z w : ℂ} (h : z.im = w.im) : edist z w = edist z.re w.re := by
   rw [edist_nndist, edist_nndist, nndist_of_im_eq h]
 #align complex.edist_of_im_eq Complex.edist_of_im_eq
+-/
 
+#print Complex.dist_conj_self /-
 theorem dist_conj_self (z : ℂ) : dist (conj z) z = 2 * |z.im| := by
   rw [dist_of_re_eq (conj_re z), conj_im, dist_comm, Real.dist_eq, sub_neg_eq_add, ← two_mul,
     _root_.abs_mul, abs_of_pos (zero_lt_two' ℝ)]
 #align complex.dist_conj_self Complex.dist_conj_self
+-/
 
+#print Complex.nndist_conj_self /-
 theorem nndist_conj_self (z : ℂ) : nndist (conj z) z = 2 * Real.nnabs z.im :=
   NNReal.eq <| by rw [← dist_nndist, NNReal.coe_mul, NNReal.coe_two, Real.coe_nnabs, dist_conj_self]
 #align complex.nndist_conj_self Complex.nndist_conj_self
+-/
 
+#print Complex.dist_self_conj /-
 theorem dist_self_conj (z : ℂ) : dist z (conj z) = 2 * |z.im| := by rw [dist_comm, dist_conj_self]
 #align complex.dist_self_conj Complex.dist_self_conj
+-/
 
+#print Complex.nndist_self_conj /-
 theorem nndist_self_conj (z : ℂ) : nndist z (conj z) = 2 * Real.nnabs z.im := by
   rw [nndist_comm, nndist_conj_self]
 #align complex.nndist_self_conj Complex.nndist_self_conj
+-/
 
+#print Complex.comap_abs_nhds_zero /-
 @[simp]
 theorem comap_abs_nhds_zero : Filter.comap abs (𝓝 0) = 𝓝 0 :=
   comap_norm_nhds_zero
 #align complex.comap_abs_nhds_zero Complex.comap_abs_nhds_zero
+-/
 
+#print Complex.norm_real /-
 theorem norm_real (r : ℝ) : ‖(r : ℂ)‖ = ‖r‖ :=
   abs_ofReal _
 #align complex.norm_real Complex.norm_real
+-/
 
+#print Complex.norm_rat /-
 @[simp]
 theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| := by rw [← of_real_rat_cast]; exact norm_real _
 #align complex.norm_rat Complex.norm_rat
+-/
 
+#print Complex.norm_nat /-
 @[simp]
 theorem norm_nat (n : ℕ) : ‖(n : ℂ)‖ = n :=
   abs_of_nat _
 #align complex.norm_nat Complex.norm_nat
+-/
 
+#print Complex.norm_int /-
 @[simp]
 theorem norm_int {n : ℤ} : ‖(n : ℂ)‖ = |n| := by
   simp (config := { singlePass := true }) [← Rat.cast_coe_int]
 #align complex.norm_int Complex.norm_int
+-/
 
+#print Complex.norm_int_of_nonneg /-
 theorem norm_int_of_nonneg {n : ℤ} (hn : 0 ≤ n) : ‖(n : ℂ)‖ = n := by simp [hn]
 #align complex.norm_int_of_nonneg Complex.norm_int_of_nonneg
+-/
 
+#print Complex.continuous_abs /-
 @[continuity]
 theorem continuous_abs : Continuous abs :=
   continuous_norm
 #align complex.continuous_abs Complex.continuous_abs
+-/
 
+#print Complex.continuous_normSq /-
 @[continuity]
 theorem continuous_normSq : Continuous normSq := by
   simpa [← norm_sq_eq_abs] using continuous_abs.pow 2
 #align complex.continuous_norm_sq Complex.continuous_normSq
+-/
 
+#print Complex.nnnorm_real /-
 @[simp, norm_cast]
 theorem nnnorm_real (r : ℝ) : ‖(r : ℂ)‖₊ = ‖r‖₊ :=
   Subtype.ext <| norm_real r
 #align complex.nnnorm_real Complex.nnnorm_real
+-/
 
+#print Complex.nnnorm_nat /-
 @[simp, norm_cast]
 theorem nnnorm_nat (n : ℕ) : ‖(n : ℂ)‖₊ = n :=
   Subtype.ext <| by simp
 #align complex.nnnorm_nat Complex.nnnorm_nat
+-/
 
+#print Complex.nnnorm_int /-
 @[simp, norm_cast]
 theorem nnnorm_int (n : ℤ) : ‖(n : ℂ)‖₊ = ‖n‖₊ :=
   Subtype.ext <| by simp only [coe_nnnorm, norm_int, Int.norm_eq_abs]
 #align complex.nnnorm_int Complex.nnnorm_int
+-/
 
+#print Complex.nnnorm_eq_one_of_pow_eq_one /-
 theorem nnnorm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖₊ = 1 :=
   by
   refine' (@pow_left_inj NNReal _ _ _ _ zero_le' zero_le' hn.bot_lt).mp _
   rw [← nnnorm_pow, h, nnnorm_one, one_pow]
 #align complex.nnnorm_eq_one_of_pow_eq_one Complex.nnnorm_eq_one_of_pow_eq_one
+-/
 
+#print Complex.norm_eq_one_of_pow_eq_one /-
 theorem norm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖ = 1 :=
   congr_arg coe (nnnorm_eq_one_of_pow_eq_one h hn)
 #align complex.norm_eq_one_of_pow_eq_one Complex.norm_eq_one_of_pow_eq_one
+-/
 
+#print Complex.equivRealProd_apply_le /-
 theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ abs z := by
   simp [Prod.norm_def, abs_re_le_abs, abs_im_le_abs]
 #align complex.equiv_real_prod_apply_le Complex.equivRealProd_apply_le
+-/
 
+#print Complex.equivRealProd_apply_le' /-
 theorem equivRealProd_apply_le' (z : ℂ) : ‖equivRealProd z‖ ≤ 1 * abs z := by
   simpa using equiv_real_prod_apply_le z
 #align complex.equiv_real_prod_apply_le' Complex.equivRealProd_apply_le'
+-/
 
 #print Complex.lipschitz_equivRealProd /-
 theorem lipschitz_equivRealProd : LipschitzWith 1 equivRealProd := by
@@ -233,19 +295,23 @@ theorem antilipschitz_equivRealProd : AntilipschitzWith (NNReal.sqrt 2) equivRea
 #align complex.antilipschitz_equiv_real_prod Complex.antilipschitz_equivRealProd
 -/
 
+#print Complex.uniformEmbedding_equivRealProd /-
 theorem uniformEmbedding_equivRealProd : UniformEmbedding equivRealProd :=
   antilipschitz_equivRealProd.UniformEmbedding lipschitz_equivRealProd.UniformContinuous
 #align complex.uniform_embedding_equiv_real_prod Complex.uniformEmbedding_equivRealProd
+-/
 
 instance : CompleteSpace ℂ :=
   (completeSpace_congr uniformEmbedding_equivRealProd).mpr inferInstance
 
+#print Complex.equivRealProdClm /-
 /-- The natural `continuous_linear_equiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
 def equivRealProdClm : ℂ ≃L[ℝ] ℝ × ℝ :=
   equivRealProdLm.toContinuousLinearEquivOfBounds 1 (Real.sqrt 2) equivRealProd_apply_le' fun p =>
     abs_le_sqrt_two_mul_max (equivRealProd.symm p)
 #align complex.equiv_real_prod_clm Complex.equivRealProdClm
+-/
 
 instance : ProperSpace ℂ :=
   (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdClm.toHomeomorph).ProperSpace
@@ -268,102 +334,141 @@ theorem tendsto_normSq_cocompact_atTop : Filter.Tendsto normSq (Filter.cocompact
 
 open ContinuousLinearMap
 
+#print Complex.reClm /-
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
 def reClm : ℂ →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by simp [abs_re_le_abs]
 #align complex.re_clm Complex.reClm
+-/
 
+#print Complex.continuous_re /-
 @[continuity]
 theorem continuous_re : Continuous re :=
   reClm.Continuous
 #align complex.continuous_re Complex.continuous_re
+-/
 
+#print Complex.reClm_coe /-
 @[simp]
 theorem reClm_coe : (coe reClm : ℂ →ₗ[ℝ] ℝ) = reLm :=
   rfl
 #align complex.re_clm_coe Complex.reClm_coe
+-/
 
+#print Complex.reClm_apply /-
 @[simp]
 theorem reClm_apply (z : ℂ) : (reClm : ℂ → ℝ) z = z.re :=
   rfl
 #align complex.re_clm_apply Complex.reClm_apply
+-/
 
+#print Complex.imClm /-
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
 def imClm : ℂ →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by simp [abs_im_le_abs]
 #align complex.im_clm Complex.imClm
+-/
 
+#print Complex.continuous_im /-
 @[continuity]
 theorem continuous_im : Continuous im :=
   imClm.Continuous
 #align complex.continuous_im Complex.continuous_im
+-/
 
+#print Complex.imClm_coe /-
 @[simp]
 theorem imClm_coe : (coe imClm : ℂ →ₗ[ℝ] ℝ) = imLm :=
   rfl
 #align complex.im_clm_coe Complex.imClm_coe
+-/
 
+#print Complex.imClm_apply /-
 @[simp]
 theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
   rfl
 #align complex.im_clm_apply Complex.imClm_apply
+-/
 
+#print Complex.restrictScalars_one_smulRight' /-
 theorem restrictScalars_one_smulRight' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =
       reClm.smul_right x + I • imClm.smul_right x :=
   by ext ⟨a, b⟩; simp [mk_eq_add_mul_I, add_smul, mul_smul, smul_comm I]
 #align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'
+-/
 
+#print Complex.restrictScalars_one_smulRight /-
 theorem restrictScalars_one_smulRight (x : ℂ) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] ℂ) = x • 1 := by
   ext1 z; dsimp; apply mul_comm
 #align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRight
+-/
 
+#print Complex.conjLie /-
 /-- The complex-conjugation function from `ℂ` to itself is an isometric linear equivalence. -/
 def conjLie : ℂ ≃ₗᵢ[ℝ] ℂ :=
   ⟨conjAe.toLinearEquiv, abs_conj⟩
 #align complex.conj_lie Complex.conjLie
+-/
 
+#print Complex.conjLie_apply /-
 @[simp]
 theorem conjLie_apply (z : ℂ) : conjLie z = conj z :=
   rfl
 #align complex.conj_lie_apply Complex.conjLie_apply
+-/
 
+#print Complex.conjLie_symm /-
 @[simp]
 theorem conjLie_symm : conjLie.symm = conjLie :=
   rfl
 #align complex.conj_lie_symm Complex.conjLie_symm
+-/
 
+#print Complex.isometry_conj /-
 theorem isometry_conj : Isometry (conj : ℂ → ℂ) :=
   conjLie.Isometry
 #align complex.isometry_conj Complex.isometry_conj
+-/
 
+#print Complex.dist_conj_conj /-
 @[simp]
 theorem dist_conj_conj (z w : ℂ) : dist (conj z) (conj w) = dist z w :=
   isometry_conj.dist_eq z w
 #align complex.dist_conj_conj Complex.dist_conj_conj
+-/
 
+#print Complex.nndist_conj_conj /-
 @[simp]
 theorem nndist_conj_conj (z w : ℂ) : nndist (conj z) (conj w) = nndist z w :=
   isometry_conj.nndist_eq z w
 #align complex.nndist_conj_conj Complex.nndist_conj_conj
+-/
 
+#print Complex.dist_conj_comm /-
 theorem dist_conj_comm (z w : ℂ) : dist (conj z) w = dist z (conj w) := by
   rw [← dist_conj_conj, conj_conj]
 #align complex.dist_conj_comm Complex.dist_conj_comm
+-/
 
+#print Complex.nndist_conj_comm /-
 theorem nndist_conj_comm (z w : ℂ) : nndist (conj z) w = nndist z (conj w) :=
   Subtype.ext <| dist_conj_comm _ _
 #align complex.nndist_conj_comm Complex.nndist_conj_comm
+-/
 
 instance : ContinuousStar ℂ :=
   ⟨conjLie.Continuous⟩
 
+#print Complex.continuous_conj /-
 @[continuity]
 theorem continuous_conj : Continuous (conj : ℂ → ℂ) :=
   continuous_star
 #align complex.continuous_conj Complex.continuous_conj
+-/
 
+#print Complex.ringHom_eq_id_or_conj_of_continuous /-
 /-- The only continuous ring homomorphisms from `ℂ` to `ℂ` are the identity and the complex
 conjugation. -/
 theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous f) :
@@ -373,36 +478,50 @@ theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous
     (real_alg_hom_eq_id_or_conj <| AlgHom.mk' f <| map_real_smul f hf).imp (fun h => _) fun h => _
   all_goals convert congr_arg AlgHom.toRingHom h; ext1; rfl
 #align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuous
+-/
 
+#print Complex.conjCle /-
 /-- Continuous linear equiv version of the conj function, from `ℂ` to `ℂ`. -/
 def conjCle : ℂ ≃L[ℝ] ℂ :=
   conjLie
 #align complex.conj_cle Complex.conjCle
+-/
 
+#print Complex.conjCle_coe /-
 @[simp]
 theorem conjCle_coe : conjCle.toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
 #align complex.conj_cle_coe Complex.conjCle_coe
+-/
 
+#print Complex.conjCle_apply /-
 @[simp]
 theorem conjCle_apply (z : ℂ) : conjCle z = conj z :=
   rfl
 #align complex.conj_cle_apply Complex.conjCle_apply
+-/
 
+#print Complex.ofRealLi /-
 /-- Linear isometry version of the canonical embedding of `ℝ` in `ℂ`. -/
 def ofRealLi : ℝ →ₗᵢ[ℝ] ℂ :=
   ⟨ofRealAm.toLinearMap, norm_real⟩
 #align complex.of_real_li Complex.ofRealLi
+-/
 
+#print Complex.isometry_ofReal /-
 theorem isometry_ofReal : Isometry (coe : ℝ → ℂ) :=
   ofRealLi.Isometry
 #align complex.isometry_of_real Complex.isometry_ofReal
+-/
 
+#print Complex.continuous_ofReal /-
 @[continuity]
 theorem continuous_ofReal : Continuous (coe : ℝ → ℂ) :=
   ofRealLi.Continuous
 #align complex.continuous_of_real Complex.continuous_ofReal
+-/
 
+#print Complex.ringHom_eq_ofReal_of_continuous /-
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
 theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) : f = Complex.ofReal :=
   by
@@ -411,21 +530,28 @@ theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) :
       (Subsingleton.elim (AlgHom.mk' f <| map_real_smul f h) <| Algebra.ofId ℝ ℂ)
   ext1; rfl
 #align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuous
+-/
 
+#print Complex.ofRealClm /-
 /-- Continuous linear map version of the canonical embedding of `ℝ` in `ℂ`. -/
 def ofRealClm : ℝ →L[ℝ] ℂ :=
   ofRealLi.toContinuousLinearMap
 #align complex.of_real_clm Complex.ofRealClm
+-/
 
+#print Complex.ofRealClm_coe /-
 @[simp]
 theorem ofRealClm_coe : (ofRealClm : ℝ →ₗ[ℝ] ℂ) = ofRealAm.toLinearMap :=
   rfl
 #align complex.of_real_clm_coe Complex.ofRealClm_coe
+-/
 
+#print Complex.ofRealClm_apply /-
 @[simp]
 theorem ofRealClm_apply (x : ℝ) : ofRealClm x = x :=
   rfl
 #align complex.of_real_clm_apply Complex.ofRealClm_apply
+-/
 
 noncomputable instance : IsROrC ℂ
     where
@@ -453,21 +579,27 @@ noncomputable instance : IsROrC ℂ
       Complex.norm_eq_abs]
   mul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.I_im]
 
+#print IsROrC.re_eq_complex_re /-
 theorem IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
   rfl
 #align is_R_or_C.re_eq_complex_re IsROrC.re_eq_complex_re
+-/
 
+#print IsROrC.im_eq_complex_im /-
 theorem IsROrC.im_eq_complex_im : ⇑(IsROrC.im : ℂ →+ ℝ) = Complex.im :=
   rfl
 #align is_R_or_C.im_eq_complex_im IsROrC.im_eq_complex_im
+-/
 
 section ComplexOrder
 
 open scoped ComplexOrder
 
+#print Complex.eq_coe_norm_of_nonneg /-
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
   rw [eq_re_of_real_le hz, IsROrC.norm_ofReal, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
+-/
 
 end ComplexOrder
 
@@ -477,61 +609,73 @@ namespace IsROrC
 
 open scoped ComplexConjugate
 
--- mathport name: exprreC
 local notation "reC" => @IsROrC.re ℂ _
 
--- mathport name: exprimC
 local notation "imC" => @IsROrC.im ℂ _
 
--- mathport name: exprIC
 local notation "IC" => @IsROrC.i ℂ _
 
--- mathport name: exprnorm_sqC
 local notation "norm_sqC" => @IsROrC.normSq ℂ _
 
+#print IsROrC.re_to_complex /-
 @[simp]
 theorem re_to_complex {x : ℂ} : reC x = x.re :=
   rfl
 #align is_R_or_C.re_to_complex IsROrC.re_to_complex
+-/
 
+#print IsROrC.im_to_complex /-
 @[simp]
 theorem im_to_complex {x : ℂ} : imC x = x.im :=
   rfl
 #align is_R_or_C.im_to_complex IsROrC.im_to_complex
+-/
 
+#print IsROrC.I_to_complex /-
 @[simp]
 theorem I_to_complex : IC = Complex.I :=
   rfl
 #align is_R_or_C.I_to_complex IsROrC.I_to_complex
+-/
 
+#print IsROrC.normSq_to_complex /-
 @[simp]
 theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x :=
   rfl
 #align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complex
+-/
 
 section tsum
 
 variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]
 
+#print IsROrC.hasSum_conj /-
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
   conjCle.HasSum
 #align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
+-/
 
+#print IsROrC.hasSum_conj' /-
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   conjCle.hasSum'
 #align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
+-/
 
+#print IsROrC.summable_conj /-
 @[simp]
 theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Summable f :=
   summable_star_iff
 #align is_R_or_C.summable_conj IsROrC.summable_conj
+-/
 
 variable {𝕜}
 
+#print IsROrC.conj_tsum /-
 theorem conj_tsum (f : α → 𝕜) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   tsum_star
 #align is_R_or_C.conj_tsum IsROrC.conj_tsum
+-/
 
 variable (𝕜)
 
@@ -563,24 +707,33 @@ theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, f a :
 #align is_R_or_C.of_real_tsum IsROrC.ofReal_tsum
 -/
 
+#print IsROrC.hasSum_re /-
 theorem hasSum_re {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => re (f x)) (re x) :=
   reClm.HasSum h
 #align is_R_or_C.has_sum_re IsROrC.hasSum_re
+-/
 
+#print IsROrC.hasSum_im /-
 theorem hasSum_im {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => im (f x)) (im x) :=
   imClm.HasSum h
 #align is_R_or_C.has_sum_im IsROrC.hasSum_im
+-/
 
+#print IsROrC.re_tsum /-
 theorem re_tsum {f : α → 𝕜} (h : Summable f) : re (∑' a, f a) = ∑' a, re (f a) :=
   reClm.map_tsum h
 #align is_R_or_C.re_tsum IsROrC.re_tsum
+-/
 
+#print IsROrC.im_tsum /-
 theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a, im (f a) :=
   imClm.map_tsum h
 #align is_R_or_C.im_tsum IsROrC.im_tsum
+-/
 
 variable {𝕜}
 
+#print IsROrC.hasSum_iff /-
 theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
     HasSum f c ↔ HasSum (fun x => re (f x)) (re c) ∧ HasSum (fun x => im (f x)) (im c) :=
   by
@@ -590,6 +743,7 @@ theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
   convert ((has_sum_of_real 𝕜).mpr h₁).add (((has_sum_of_real 𝕜).mpr h₂).mul_right I)
   simp_rw [IsROrC.re_add_im]
 #align is_R_or_C.has_sum_iff IsROrC.hasSum_iff
+-/
 
 end tsum
 
@@ -612,59 +766,83 @@ variable {α : Type _}
 
 open scoped ComplexConjugate
 
+#print Complex.hasSum_conj /-
 @[simp]
 theorem hasSum_conj {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
   IsROrC.hasSum_conj _
 #align complex.has_sum_conj Complex.hasSum_conj
+-/
 
+#print Complex.hasSum_conj' /-
 theorem hasSum_conj' {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   IsROrC.hasSum_conj' _
 #align complex.has_sum_conj' Complex.hasSum_conj'
+-/
 
+#print Complex.summable_conj /-
 @[simp]
 theorem summable_conj {f : α → ℂ} : (Summable fun x => conj (f x)) ↔ Summable f :=
   IsROrC.summable_conj _
 #align complex.summable_conj Complex.summable_conj
+-/
 
+#print Complex.conj_tsum /-
 theorem conj_tsum (f : α → ℂ) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   IsROrC.conj_tsum _
 #align complex.conj_tsum Complex.conj_tsum
+-/
 
+#print Complex.hasSum_ofReal /-
 @[simp, norm_cast]
 theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : ℂ)) x ↔ HasSum f x :=
   IsROrC.hasSum_ofReal _
 #align complex.has_sum_of_real Complex.hasSum_ofReal
+-/
 
+#print Complex.summable_ofReal /-
 @[simp, norm_cast]
 theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : ℂ)) ↔ Summable f :=
   IsROrC.summable_ofReal _
 #align complex.summable_of_real Complex.summable_ofReal
+-/
 
+#print Complex.ofReal_tsum /-
 @[norm_cast]
 theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : ℂ) = ∑' a, f a :=
   IsROrC.ofReal_tsum _ _
 #align complex.of_real_tsum Complex.ofReal_tsum
+-/
 
+#print Complex.hasSum_re /-
 theorem hasSum_re {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).re) x.re :=
   IsROrC.hasSum_re _ h
 #align complex.has_sum_re Complex.hasSum_re
+-/
 
+#print Complex.hasSum_im /-
 theorem hasSum_im {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).im) x.im :=
   IsROrC.hasSum_im _ h
 #align complex.has_sum_im Complex.hasSum_im
+-/
 
+#print Complex.re_tsum /-
 theorem re_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).re = ∑' a, (f a).re :=
   IsROrC.re_tsum _ h
 #align complex.re_tsum Complex.re_tsum
+-/
 
+#print Complex.im_tsum /-
 theorem im_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).im = ∑' a, (f a).im :=
   IsROrC.im_tsum _ h
 #align complex.im_tsum Complex.im_tsum
+-/
 
+#print Complex.hasSum_iff /-
 theorem hasSum_iff (f : α → ℂ) (c : ℂ) :
     HasSum f c ↔ HasSum (fun x => (f x).re) c.re ∧ HasSum (fun x => (f x).im) c.im :=
   IsROrC.hasSum_iff _ _
 #align complex.has_sum_iff Complex.hasSum_iff
+-/
 
 end tsum
 

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

@@ -406,7 +406,8 @@ theorem continuous_ofReal : Continuous (coe : ℝ → ℂ) :=
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
 theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) : f = Complex.ofReal :=
   by
-  convert congr_arg AlgHom.toRingHom
+  convert
+    congr_arg AlgHom.toRingHom
       (Subsingleton.elim (AlgHom.mk' f <| map_real_smul f h) <| Algebra.ofId ℝ ℂ)
   ext1; rfl
 #align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuous
@@ -586,7 +587,7 @@ theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
   refine' ⟨fun h => ⟨has_sum_re _ h, has_sum_im _ h⟩, _⟩
   rintro ⟨h₁, h₂⟩
   rw [← IsROrC.re_add_im c]
-  convert((has_sum_of_real 𝕜).mpr h₁).add (((has_sum_of_real 𝕜).mpr h₂).mul_right I)
+  convert ((has_sum_of_real 𝕜).mpr h₁).add (((has_sum_of_real 𝕜).mpr h₂).mul_right I)
   simp_rw [IsROrC.re_add_im]
 #align is_R_or_C.has_sum_iff IsROrC.hasSum_iff
 

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

@@ -47,7 +47,7 @@ noncomputable section
 
 namespace Complex
 
-open ComplexConjugate Topology
+open scoped ComplexConjugate Topology
 
 instance : Norm ℂ :=
   ⟨abs⟩
@@ -462,7 +462,7 @@ theorem IsROrC.im_eq_complex_im : ⇑(IsROrC.im : ℂ →+ ℝ) = Complex.im :=
 
 section ComplexOrder
 
-open ComplexOrder
+open scoped ComplexOrder
 
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
   rw [eq_re_of_real_le hz, IsROrC.norm_ofReal, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
@@ -474,7 +474,7 @@ end Complex
 
 namespace IsROrC
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 -- mathport name: exprreC
 local notation "reC" => @IsROrC.re ℂ _
@@ -609,7 +609,7 @@ section tsum
 
 variable {α : Type _}
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 @[simp]
 theorem hasSum_conj {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=

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

@@ -52,23 +52,11 @@ open ComplexConjugate Topology
 instance : Norm ℂ :=
   ⟨abs⟩
 
-/- warning: complex.norm_eq_abs -> Complex.norm_eq_abs is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align complex.norm_eq_abs Complex.norm_eq_absₓ'. -/
 @[simp]
 theorem norm_eq_abs (z : ℂ) : ‖z‖ = abs z :=
   rfl
 #align complex.norm_eq_abs Complex.norm_eq_abs
 
-/- warning: complex.norm_exp_of_real_mul_I -> Complex.norm_exp_ofReal_mul_I is a dubious translation:
-lean 3 declaration is
-  forall (t : Real), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) t) Complex.I))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
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-Case conversion may be inaccurate. Consider using '#align complex.norm_exp_of_real_mul_I Complex.norm_exp_ofReal_mul_Iₓ'. -/
 theorem norm_exp_ofReal_mul_I (t : ℝ) : ‖exp (t * I)‖ = 1 := by
   simp only [norm_eq_abs, abs_exp_of_real_mul_I]
 #align complex.norm_exp_of_real_mul_I Complex.norm_exp_ofReal_mul_I
@@ -104,305 +92,131 @@ instance {R : Type _} [NormedField R] [NormedAlgebra R ℝ] : NormedAlgebra R 
 
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
-/- warning: normed_space.complex_to_real -> NormedSpace.complexToReal is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align normed_space.complex_to_real NormedSpace.complexToRealₓ'. -/
 -- see Note [lower instance priority]
 /-- The module structure from `module.complex_to_real` is a normed space. -/
 instance (priority := 900) NormedSpace.complexToReal : NormedSpace ℝ E :=
   NormedSpace.restrictScalars ℝ ℂ E
 #align normed_space.complex_to_real NormedSpace.complexToReal
 
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-Case conversion may be inaccurate. Consider using '#align complex.dist_eq Complex.dist_eqₓ'. -/
 theorem dist_eq (z w : ℂ) : dist z w = abs (z - w) :=
   rfl
 #align complex.dist_eq Complex.dist_eq
 
-/- warning: complex.dist_eq_re_im -> Complex.dist_eq_re_im is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.dist_eq_re_im Complex.dist_eq_re_imₓ'. -/
 theorem dist_eq_re_im (z w : ℂ) : dist z w = Real.sqrt ((z.re - w.re) ^ 2 + (z.im - w.im) ^ 2) := by
   rw [sq, sq]; rfl
 #align complex.dist_eq_re_im Complex.dist_eq_re_im
 
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-Case conversion may be inaccurate. Consider using '#align complex.dist_mk Complex.dist_mkₓ'. -/
 @[simp]
 theorem dist_mk (x₁ y₁ x₂ y₂ : ℝ) :
     dist (mk x₁ y₁) (mk x₂ y₂) = Real.sqrt ((x₁ - x₂) ^ 2 + (y₁ - y₂) ^ 2) :=
   dist_eq_re_im _ _
 #align complex.dist_mk Complex.dist_mk
 
-/- warning: complex.dist_of_re_eq -> Complex.dist_of_re_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.dist_of_re_eq Complex.dist_of_re_eqₓ'. -/
 theorem dist_of_re_eq {z w : ℂ} (h : z.re = w.re) : dist z w = dist z.im w.im := by
   rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, zero_add, Real.sqrt_sq_eq_abs, Real.dist_eq]
 #align complex.dist_of_re_eq Complex.dist_of_re_eq
 
-/- warning: complex.nndist_of_re_eq -> Complex.nndist_of_re_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.nndist_of_re_eq Complex.nndist_of_re_eqₓ'. -/
 theorem nndist_of_re_eq {z w : ℂ} (h : z.re = w.re) : nndist z w = nndist z.im w.im :=
   NNReal.eq <| dist_of_re_eq h
 #align complex.nndist_of_re_eq Complex.nndist_of_re_eq
 
-/- warning: complex.edist_of_re_eq -> Complex.edist_of_re_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.edist_of_re_eq Complex.edist_of_re_eqₓ'. -/
 theorem edist_of_re_eq {z w : ℂ} (h : z.re = w.re) : edist z w = edist z.im w.im := by
   rw [edist_nndist, edist_nndist, nndist_of_re_eq h]
 #align complex.edist_of_re_eq Complex.edist_of_re_eq
 
-/- warning: complex.dist_of_im_eq -> Complex.dist_of_im_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.dist_of_im_eq Complex.dist_of_im_eqₓ'. -/
 theorem dist_of_im_eq {z w : ℂ} (h : z.im = w.im) : dist z w = dist z.re w.re := by
   rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, add_zero, Real.sqrt_sq_eq_abs, Real.dist_eq]
 #align complex.dist_of_im_eq Complex.dist_of_im_eq
 
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-Case conversion may be inaccurate. Consider using '#align complex.nndist_of_im_eq Complex.nndist_of_im_eqₓ'. -/
 theorem nndist_of_im_eq {z w : ℂ} (h : z.im = w.im) : nndist z w = nndist z.re w.re :=
   NNReal.eq <| dist_of_im_eq h
 #align complex.nndist_of_im_eq Complex.nndist_of_im_eq
 
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-Case conversion may be inaccurate. Consider using '#align complex.edist_of_im_eq Complex.edist_of_im_eqₓ'. -/
 theorem edist_of_im_eq {z w : ℂ} (h : z.im = w.im) : edist z w = edist z.re w.re := by
   rw [edist_nndist, edist_nndist, nndist_of_im_eq h]
 #align complex.edist_of_im_eq Complex.edist_of_im_eq
 
-/- warning: complex.dist_conj_self -> Complex.dist_conj_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.dist_conj_self Complex.dist_conj_selfₓ'. -/
 theorem dist_conj_self (z : ℂ) : dist (conj z) z = 2 * |z.im| := by
   rw [dist_of_re_eq (conj_re z), conj_im, dist_comm, Real.dist_eq, sub_neg_eq_add, ← two_mul,
     _root_.abs_mul, abs_of_pos (zero_lt_two' ℝ)]
 #align complex.dist_conj_self Complex.dist_conj_self
 
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-Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_self Complex.nndist_conj_selfₓ'. -/
 theorem nndist_conj_self (z : ℂ) : nndist (conj z) z = 2 * Real.nnabs z.im :=
   NNReal.eq <| by rw [← dist_nndist, NNReal.coe_mul, NNReal.coe_two, Real.coe_nnabs, dist_conj_self]
 #align complex.nndist_conj_self Complex.nndist_conj_self
 
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-Case conversion may be inaccurate. Consider using '#align complex.dist_self_conj Complex.dist_self_conjₓ'. -/
 theorem dist_self_conj (z : ℂ) : dist z (conj z) = 2 * |z.im| := by rw [dist_comm, dist_conj_self]
 #align complex.dist_self_conj Complex.dist_self_conj
 
-/- warning: complex.nndist_self_conj -> Complex.nndist_self_conj is a dubious translation:
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Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} NNReal ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) (Complex.im z)) NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Complex.im z)))
-Case conversion may be inaccurate. Consider using '#align complex.nndist_self_conj Complex.nndist_self_conjₓ'. -/
 theorem nndist_self_conj (z : ℂ) : nndist z (conj z) = 2 * Real.nnabs z.im := by
   rw [nndist_comm, nndist_conj_self]
 #align complex.nndist_self_conj Complex.nndist_self_conj
 
-/- warning: complex.comap_abs_nhds_zero -> Complex.comap_abs_nhds_zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align complex.comap_abs_nhds_zero Complex.comap_abs_nhds_zeroₓ'. -/
 @[simp]
 theorem comap_abs_nhds_zero : Filter.comap abs (𝓝 0) = 𝓝 0 :=
   comap_norm_nhds_zero
 #align complex.comap_abs_nhds_zero Complex.comap_abs_nhds_zero
 
-/- warning: complex.norm_real -> Complex.norm_real is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (Norm.norm.{0} Real Real.hasNorm r)
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-  forall (r : Real), Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Complex.ofReal' r)) (Norm.norm.{0} Real Real.norm r)
-Case conversion may be inaccurate. Consider using '#align complex.norm_real Complex.norm_realₓ'. -/
 theorem norm_real (r : ℝ) : ‖(r : ℂ)‖ = ‖r‖ :=
   abs_ofReal _
 #align complex.norm_real Complex.norm_real
 
-/- warning: complex.norm_rat -> Complex.norm_rat is a dubious translation:
-lean 3 declaration is
-  forall (r : Rat), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (NormedDivisionRing.toDivisionRing.{0} Complex (NormedField.toNormedDivisionRing.{0} Complex Complex.normedField)))))) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) r))
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-Case conversion may be inaccurate. Consider using '#align complex.norm_rat Complex.norm_ratₓ'. -/
 @[simp]
 theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| := by rw [← of_real_rat_cast]; exact norm_real _
 #align complex.norm_rat Complex.norm_rat
 
-/- warning: complex.norm_nat -> Complex.norm_nat is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
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-Case conversion may be inaccurate. Consider using '#align complex.norm_nat Complex.norm_natₓ'. -/
 @[simp]
 theorem norm_nat (n : ℕ) : ‖(n : ℂ)‖ = n :=
   abs_of_nat _
 #align complex.norm_nat Complex.norm_nat
 
-/- warning: complex.norm_int -> Complex.norm_int is a dubious translation:
-lean 3 declaration is
-  forall {n : Int}, Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n))
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-  forall {n : Int}, Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Int.cast.{0} Real Real.intCast n))
-Case conversion may be inaccurate. Consider using '#align complex.norm_int Complex.norm_intₓ'. -/
 @[simp]
 theorem norm_int {n : ℤ} : ‖(n : ℂ)‖ = |n| := by
   simp (config := { singlePass := true }) [← Rat.cast_coe_int]
 #align complex.norm_int Complex.norm_int
 
-/- warning: complex.norm_int_of_nonneg -> Complex.norm_int_of_nonneg is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align complex.norm_int_of_nonneg Complex.norm_int_of_nonnegₓ'. -/
 theorem norm_int_of_nonneg {n : ℤ} (hn : 0 ≤ n) : ‖(n : ℂ)‖ = n := by simp [hn]
 #align complex.norm_int_of_nonneg Complex.norm_int_of_nonneg
 
-/- warning: complex.continuous_abs -> Complex.continuous_abs is a dubious translation:
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-  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)
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-Case conversion may be inaccurate. Consider using '#align complex.continuous_abs Complex.continuous_absₓ'. -/
 @[continuity]
 theorem continuous_abs : Continuous abs :=
   continuous_norm
 #align complex.continuous_abs Complex.continuous_abs
 
-/- warning: complex.continuous_norm_sq -> Complex.continuous_normSq is a dubious translation:
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 @[continuity]
 theorem continuous_normSq : Continuous normSq := by
   simpa [← norm_sq_eq_abs] using continuous_abs.pow 2
 #align complex.continuous_norm_sq Complex.continuous_normSq
 
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 @[simp, norm_cast]
 theorem nnnorm_real (r : ℝ) : ‖(r : ℂ)‖₊ = ‖r‖₊ :=
   Subtype.ext <| norm_real r
 #align complex.nnnorm_real Complex.nnnorm_real
 
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 @[simp, norm_cast]
 theorem nnnorm_nat (n : ℕ) : ‖(n : ℂ)‖₊ = n :=
   Subtype.ext <| by simp
 #align complex.nnnorm_nat Complex.nnnorm_nat
 
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 @[simp, norm_cast]
 theorem nnnorm_int (n : ℤ) : ‖(n : ℂ)‖₊ = ‖n‖₊ :=
   Subtype.ext <| by simp only [coe_nnnorm, norm_int, Int.norm_eq_abs]
 #align complex.nnnorm_int Complex.nnnorm_int
 
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 theorem nnnorm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖₊ = 1 :=
   by
   refine' (@pow_left_inj NNReal _ _ _ _ zero_le' zero_le' hn.bot_lt).mp _
   rw [← nnnorm_pow, h, nnnorm_one, one_pow]
 #align complex.nnnorm_eq_one_of_pow_eq_one Complex.nnnorm_eq_one_of_pow_eq_one
 
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 theorem norm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖ = 1 :=
   congr_arg coe (nnnorm_eq_one_of_pow_eq_one h hn)
 #align complex.norm_eq_one_of_pow_eq_one Complex.norm_eq_one_of_pow_eq_one
 
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 theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ abs z := by
   simp [Prod.norm_def, abs_re_le_abs, abs_im_le_abs]
 #align complex.equiv_real_prod_apply_le Complex.equivRealProd_apply_le
 
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-Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_apply_le' Complex.equivRealProd_apply_le'ₓ'. -/
 theorem equivRealProd_apply_le' (z : ℂ) : ‖equivRealProd z‖ ≤ 1 * abs z := by
   simpa using equiv_real_prod_apply_le z
 #align complex.equiv_real_prod_apply_le' Complex.equivRealProd_apply_le'
@@ -419,12 +233,6 @@ theorem antilipschitz_equivRealProd : AntilipschitzWith (NNReal.sqrt 2) equivRea
 #align complex.antilipschitz_equiv_real_prod Complex.antilipschitz_equivRealProd
 -/
 
-/- warning: complex.uniform_embedding_equiv_real_prod -> Complex.uniformEmbedding_equivRealProd is a dubious translation:
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-  UniformEmbedding.{0, 0} Complex (Prod.{0, 0} Real Real) (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Prod.uniformSpace.{0, 0} Real Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) (fun (_x : Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) => Complex -> (Prod.{0, 0} Real Real)) (Equiv.hasCoeToFun.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd)
-but is expected to have type
-  UniformEmbedding.{0, 0} Complex (Prod.{0, 0} Real Real) (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (instUniformSpaceProd.{0, 0} Real Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd)
-Case conversion may be inaccurate. Consider using '#align complex.uniform_embedding_equiv_real_prod Complex.uniformEmbedding_equivRealProdₓ'. -/
 theorem uniformEmbedding_equivRealProd : UniformEmbedding equivRealProd :=
   antilipschitz_equivRealProd.UniformEmbedding lipschitz_equivRealProd.UniformContinuous
 #align complex.uniform_embedding_equiv_real_prod Complex.uniformEmbedding_equivRealProd
@@ -432,12 +240,6 @@ theorem uniformEmbedding_equivRealProd : UniformEmbedding equivRealProd :=
 instance : CompleteSpace ℂ :=
   (completeSpace_congr uniformEmbedding_equivRealProd).mpr inferInstance
 
-/- warning: complex.equiv_real_prod_clm -> Complex.equivRealProdClm is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_clm Complex.equivRealProdClmₓ'. -/
 /-- The natural `continuous_linear_equiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
 def equivRealProdClm : ℂ ≃L[ℝ] ℝ × ℝ :=
@@ -466,183 +268,90 @@ theorem tendsto_normSq_cocompact_atTop : Filter.Tendsto normSq (Filter.cocompact
 
 open ContinuousLinearMap
 
-/- warning: complex.re_clm -> Complex.reClm is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.re_clm Complex.reClmₓ'. -/
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
 def reClm : ℂ →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by simp [abs_re_le_abs]
 #align complex.re_clm Complex.reClm
 
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-Case conversion may be inaccurate. Consider using '#align complex.continuous_re Complex.continuous_reₓ'. -/
 @[continuity]
 theorem continuous_re : Continuous re :=
   reClm.Continuous
 #align complex.continuous_re Complex.continuous_re
 
-/- warning: complex.re_clm_coe -> Complex.reClm_coe is a dubious translation:
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Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module)))) Complex.reClm) Complex.reLm
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-Case conversion may be inaccurate. Consider using '#align complex.re_clm_coe Complex.reClm_coeₓ'. -/
 @[simp]
 theorem reClm_coe : (coe reClm : ℂ →ₗ[ℝ] ℝ) = reLm :=
   rfl
 #align complex.re_clm_coe Complex.reClm_coe
 
-/- warning: complex.re_clm_apply -> Complex.reClm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.re_clm_apply Complex.reClm_applyₓ'. -/
 @[simp]
 theorem reClm_apply (z : ℂ) : (reClm : ℂ → ℝ) z = z.re :=
   rfl
 #align complex.re_clm_apply Complex.reClm_apply
 
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-Case conversion may be inaccurate. Consider using '#align complex.im_clm Complex.imClmₓ'. -/
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
 def imClm : ℂ →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by simp [abs_im_le_abs]
 #align complex.im_clm Complex.imClm
 
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-Case conversion may be inaccurate. Consider using '#align complex.continuous_im Complex.continuous_imₓ'. -/
 @[continuity]
 theorem continuous_im : Continuous im :=
   imClm.Continuous
 #align complex.continuous_im Complex.continuous_im
 
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-Case conversion may be inaccurate. Consider using '#align complex.im_clm_coe Complex.imClm_coeₓ'. -/
 @[simp]
 theorem imClm_coe : (coe imClm : ℂ →ₗ[ℝ] ℝ) = imLm :=
   rfl
 #align complex.im_clm_coe Complex.imClm_coe
 
-/- warning: complex.im_clm_apply -> Complex.imClm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.im_clm_apply Complex.imClm_applyₓ'. -/
 @[simp]
 theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
   rfl
 #align complex.im_clm_apply Complex.imClm_apply
 
-/- warning: complex.restrict_scalars_one_smul_right' -> Complex.restrictScalars_one_smulRight' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'ₓ'. -/
 theorem restrictScalars_one_smulRight' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =
       reClm.smul_right x + I • imClm.smul_right x :=
   by ext ⟨a, b⟩; simp [mk_eq_add_mul_I, add_smul, mul_smul, smul_comm I]
 #align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'
 
-/- warning: complex.restrict_scalars_one_smul_right -> Complex.restrictScalars_one_smulRight is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRightₓ'. -/
 theorem restrictScalars_one_smulRight (x : ℂ) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] ℂ) = x • 1 := by
   ext1 z; dsimp; apply mul_comm
 #align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRight
 
-/- warning: complex.conj_lie -> Complex.conjLie is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.conj_lie Complex.conjLieₓ'. -/
 /-- The complex-conjugation function from `ℂ` to itself is an isometric linear equivalence. -/
 def conjLie : ℂ ≃ₗᵢ[ℝ] ℂ :=
   ⟨conjAe.toLinearEquiv, abs_conj⟩
 #align complex.conj_lie Complex.conjLie
 
-/- warning: complex.conj_lie_apply -> Complex.conjLie_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.conj_lie_apply Complex.conjLie_applyₓ'. -/
 @[simp]
 theorem conjLie_apply (z : ℂ) : conjLie z = conj z :=
   rfl
 #align complex.conj_lie_apply Complex.conjLie_apply
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_lie_symm Complex.conjLie_symmₓ'. -/
 @[simp]
 theorem conjLie_symm : conjLie.symm = conjLie :=
   rfl
 #align complex.conj_lie_symm Complex.conjLie_symm
 
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-Case conversion may be inaccurate. Consider using '#align complex.isometry_conj Complex.isometry_conjₓ'. -/
 theorem isometry_conj : Isometry (conj : ℂ → ℂ) :=
   conjLie.Isometry
 #align complex.isometry_conj Complex.isometry_conj
 
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-Case conversion may be inaccurate. Consider using '#align complex.dist_conj_conj Complex.dist_conj_conjₓ'. -/
 @[simp]
 theorem dist_conj_conj (z w : ℂ) : dist (conj z) (conj w) = dist z w :=
   isometry_conj.dist_eq z w
 #align complex.dist_conj_conj Complex.dist_conj_conj
 
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-Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_conj Complex.nndist_conj_conjₓ'. -/
 @[simp]
 theorem nndist_conj_conj (z w : ℂ) : nndist (conj z) (conj w) = nndist z w :=
   isometry_conj.nndist_eq z w
 #align complex.nndist_conj_conj Complex.nndist_conj_conj
 
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-Case conversion may be inaccurate. Consider using '#align complex.dist_conj_comm Complex.dist_conj_commₓ'. -/
 theorem dist_conj_comm (z w : ℂ) : dist (conj z) w = dist z (conj w) := by
   rw [← dist_conj_conj, conj_conj]
 #align complex.dist_conj_comm Complex.dist_conj_comm
 
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-Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_comm Complex.nndist_conj_commₓ'. -/
 theorem nndist_conj_comm (z w : ℂ) : nndist (conj z) w = nndist z (conj w) :=
   Subtype.ext <| dist_conj_comm _ _
 #align complex.nndist_conj_comm Complex.nndist_conj_comm
@@ -650,23 +359,11 @@ theorem nndist_conj_comm (z w : ℂ) : nndist (conj z) w = nndist z (conj w) :=
 instance : ContinuousStar ℂ :=
   ⟨conjLie.Continuous⟩
 
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-Case conversion may be inaccurate. Consider using '#align complex.continuous_conj Complex.continuous_conjₓ'. -/
 @[continuity]
 theorem continuous_conj : Continuous (conj : ℂ → ℂ) :=
   continuous_star
 #align complex.continuous_conj Complex.continuous_conj
 
-/- warning: complex.ring_hom_eq_id_or_conj_of_continuous -> Complex.ringHom_eq_id_or_conj_of_continuous is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuousₓ'. -/
 /-- The only continuous ring homomorphisms from `ℂ` to `ℂ` are the identity and the complex
 conjugation. -/
 theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous f) :
@@ -677,74 +374,35 @@ theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous
   all_goals convert congr_arg AlgHom.toRingHom h; ext1; rfl
 #align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuous
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_cle Complex.conjCleₓ'. -/
 /-- Continuous linear equiv version of the conj function, from `ℂ` to `ℂ`. -/
 def conjCle : ℂ ≃L[ℝ] ℂ :=
   conjLie
 #align complex.conj_cle Complex.conjCle
 
-/- warning: complex.conj_cle_coe -> Complex.conjCle_coe is a dubious translation:
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-  Eq.{1} (LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (ContinuousLinearEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) Complex.conjCle) (AlgEquiv.toLinearEquiv.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) Complex.conjAe)
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-Case conversion may be inaccurate. Consider using '#align complex.conj_cle_coe Complex.conjCle_coeₓ'. -/
 @[simp]
 theorem conjCle_coe : conjCle.toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
 #align complex.conj_cle_coe Complex.conjCle_coe
 
-/- warning: complex.conj_cle_apply -> Complex.conjCle_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.conj_cle_apply Complex.conjCle_applyₓ'. -/
 @[simp]
 theorem conjCle_apply (z : ℂ) : conjCle z = conj z :=
   rfl
 #align complex.conj_cle_apply Complex.conjCle_apply
 
-/- warning: complex.of_real_li -> Complex.ofRealLi is a dubious translation:
-lean 3 declaration is
-  LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) Real.module (Complex.module.{0} Real Real.semiring Real.module)
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-  LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_li Complex.ofRealLiₓ'. -/
 /-- Linear isometry version of the canonical embedding of `ℝ` in `ℂ`. -/
 def ofRealLi : ℝ →ₗᵢ[ℝ] ℂ :=
   ⟨ofRealAm.toLinearMap, norm_real⟩
 #align complex.of_real_li Complex.ofRealLi
 
-/- warning: complex.isometry_of_real -> Complex.isometry_ofReal is a dubious translation:
-lean 3 declaration is
-  Isometry.{0, 0} Real Complex (PseudoMetricSpace.toPseudoEMetricSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toPseudoEMetricSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))))
-but is expected to have type
-  Isometry.{0, 0} Real Complex (EMetricSpace.toPseudoEMetricSpace.{0} Real (MetricSpace.toEMetricSpace.{0} Real Real.metricSpace)) (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex))) Complex.ofReal'
-Case conversion may be inaccurate. Consider using '#align complex.isometry_of_real Complex.isometry_ofRealₓ'. -/
 theorem isometry_ofReal : Isometry (coe : ℝ → ℂ) :=
   ofRealLi.Isometry
 #align complex.isometry_of_real Complex.isometry_ofReal
 
-/- warning: complex.continuous_of_real -> Complex.continuous_ofReal is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))))
-but is expected to have type
-  Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.ofReal'
-Case conversion may be inaccurate. Consider using '#align complex.continuous_of_real Complex.continuous_ofRealₓ'. -/
 @[continuity]
 theorem continuous_ofReal : Continuous (coe : ℝ → ℂ) :=
   ofRealLi.Continuous
 #align complex.continuous_of_real Complex.continuous_ofReal
 
-/- warning: complex.ring_hom_eq_of_real_of_continuous -> Complex.ringHom_eq_ofReal_of_continuous is a dubious translation:
-lean 3 declaration is
-  forall {f : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))}, (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (coeFn.{1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Real -> Complex) (RingHom.hasCoeToFun.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f)) -> (Eq.{1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f Complex.ofReal)
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-Case conversion may be inaccurate. Consider using '#align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuousₓ'. -/
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
 theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) : f = Complex.ofReal :=
   by
@@ -753,31 +411,16 @@ theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) :
   ext1; rfl
 #align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuous
 
-/- warning: complex.of_real_clm -> Complex.ofRealClm is a dubious translation:
-lean 3 declaration is
-  ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)
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-  ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_clm Complex.ofRealClmₓ'. -/
 /-- Continuous linear map version of the canonical embedding of `ℝ` in `ℂ`. -/
 def ofRealClm : ℝ →L[ℝ] ℂ :=
   ofRealLi.toContinuousLinearMap
 #align complex.of_real_clm Complex.ofRealClm
 
-/- warning: complex.of_real_clm_coe -> Complex.ofRealClm_coe is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (HasLiftT.mk.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (CoeTCₓ.coe.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (coeBase.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (ContinuousLinearMap.LinearMap.coe.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module))))) Complex.ofRealClm) (AlgHom.toLinearMap.{0, 0, 0} Real Real Complex Real.commSemiring Real.semiring (Ring.toSemiring.{0} Complex Complex.ring) (Algebra.id.{0} Real Real.commSemiring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) Complex.ofRealAm)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align complex.of_real_clm_coe Complex.ofRealClm_coeₓ'. -/
 @[simp]
 theorem ofRealClm_coe : (ofRealClm : ℝ →ₗ[ℝ] ℂ) = ofRealAm.toLinearMap :=
   rfl
 #align complex.of_real_clm_coe Complex.ofRealClm_coe
 
-/- warning: complex.of_real_clm_apply -> Complex.ofRealClm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.of_real_clm_apply Complex.ofRealClm_applyₓ'. -/
 @[simp]
 theorem ofRealClm_apply (x : ℝ) : ofRealClm x = x :=
   rfl
@@ -809,22 +452,10 @@ noncomputable instance : IsROrC ℂ
       Complex.norm_eq_abs]
   mul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.I_im]
 
-/- warning: is_R_or_C.re_eq_complex_re -> IsROrC.re_eq_complex_re is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_complex_re IsROrC.re_eq_complex_reₓ'. -/
 theorem IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
   rfl
 #align is_R_or_C.re_eq_complex_re IsROrC.re_eq_complex_re
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_complex_im IsROrC.im_eq_complex_imₓ'. -/
 theorem IsROrC.im_eq_complex_im : ⇑(IsROrC.im : ℂ →+ ℝ) = Complex.im :=
   rfl
 #align is_R_or_C.im_eq_complex_im IsROrC.im_eq_complex_im
@@ -833,12 +464,6 @@ section ComplexOrder
 
 open ComplexOrder
 
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-  forall {z : Complex}, (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Norm.norm.{0} Complex Complex.hasNorm z)))
-but is expected to have type
-  forall {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) z) -> (Eq.{1} Complex z (Complex.ofReal' (Norm.norm.{0} Complex Complex.instNormComplex z)))
-Case conversion may be inaccurate. Consider using '#align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonnegₓ'. -/
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
   rw [eq_re_of_real_le hz, IsROrC.norm_ofReal, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
@@ -863,45 +488,21 @@ local notation "IC" => @IsROrC.i ℂ _
 -- mathport name: exprnorm_sqC
 local notation "norm_sqC" => @IsROrC.normSq ℂ _
 
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 @[simp]
 theorem re_to_complex {x : ℂ} : reC x = x.re :=
   rfl
 #align is_R_or_C.re_to_complex IsROrC.re_to_complex
 
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 @[simp]
 theorem im_to_complex {x : ℂ} : imC x = x.im :=
   rfl
 #align is_R_or_C.im_to_complex IsROrC.im_to_complex
 
-/- warning: is_R_or_C.I_to_complex -> IsROrC.I_to_complex is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Complex (IsROrC.i.{0} Complex Complex.isROrC) Complex.I
-but is expected to have type
-  Eq.{1} Complex (IsROrC.I.{0} Complex Complex.instIsROrCComplex) Complex.I
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_to_complex IsROrC.I_to_complexₓ'. -/
 @[simp]
 theorem I_to_complex : IC = Complex.I :=
   rfl
 #align is_R_or_C.I_to_complex IsROrC.I_to_complex
 
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(MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real 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(MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq x)
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complexₓ'. -/
 @[simp]
 theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x :=
   rfl
@@ -911,27 +512,15 @@ section tsum
 
 variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]
 
-/- warning: is_R_or_C.has_sum_conj -> IsROrC.hasSum_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_conj IsROrC.hasSum_conjₓ'. -/
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
   conjCle.HasSum
 #align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
 
-/- warning: is_R_or_C.has_sum_conj' -> IsROrC.hasSum_conj' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'ₓ'. -/
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   conjCle.hasSum'
 #align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
 
-/- warning: is_R_or_C.summable_conj -> IsROrC.summable_conj is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 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(RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x))) (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f)
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.summable_conj IsROrC.summable_conjₓ'. -/
 @[simp]
 theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Summable f :=
   summable_star_iff
@@ -939,9 +528,6 @@ theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Sum
 
 variable {𝕜}
 
-/- warning: is_R_or_C.conj_tsum -> IsROrC.conj_tsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_tsum IsROrC.conj_tsumₓ'. -/
 theorem conj_tsum (f : α → 𝕜) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   tsum_star
 #align is_R_or_C.conj_tsum IsROrC.conj_tsum
@@ -976,39 +562,24 @@ theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, f a :
 #align is_R_or_C.of_real_tsum IsROrC.ofReal_tsum
 -/
 
-/- warning: is_R_or_C.has_sum_re -> IsROrC.hasSum_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_re IsROrC.hasSum_reₓ'. -/
 theorem hasSum_re {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => re (f x)) (re x) :=
   reClm.HasSum h
 #align is_R_or_C.has_sum_re IsROrC.hasSum_re
 
-/- warning: is_R_or_C.has_sum_im -> IsROrC.hasSum_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_im IsROrC.hasSum_imₓ'. -/
 theorem hasSum_im {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => im (f x)) (im x) :=
   imClm.HasSum h
 #align is_R_or_C.has_sum_im IsROrC.hasSum_im
 
-/- warning: is_R_or_C.re_tsum -> IsROrC.re_tsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_tsum IsROrC.re_tsumₓ'. -/
 theorem re_tsum {f : α → 𝕜} (h : Summable f) : re (∑' a, f a) = ∑' a, re (f a) :=
   reClm.map_tsum h
 #align is_R_or_C.re_tsum IsROrC.re_tsum
 
-/- warning: is_R_or_C.im_tsum -> IsROrC.im_tsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_tsum IsROrC.im_tsumₓ'. -/
 theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a, im (f a) :=
   imClm.map_tsum h
 #align is_R_or_C.im_tsum IsROrC.im_tsum
 
 variable {𝕜}
 
-/- warning: is_R_or_C.has_sum_iff -> IsROrC.hasSum_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_iff IsROrC.hasSum_iffₓ'. -/
 theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
     HasSum f c ↔ HasSum (fun x => re (f x)) (re c) ∧ HasSum (fun x => im (f x)) (im c) :=
   by
@@ -1040,124 +611,55 @@ variable {α : Type _}
 
 open ComplexConjugate
 
-/- warning: complex.has_sum_conj -> Complex.hasSum_conj is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x)) x) (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x))
-but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x)) x) (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x))
-Case conversion may be inaccurate. Consider using '#align complex.has_sum_conj Complex.hasSum_conjₓ'. -/
 @[simp]
 theorem hasSum_conj {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
   IsROrC.hasSum_conj _
 #align complex.has_sum_conj Complex.hasSum_conj
 
-/- warning: complex.has_sum_conj' -> Complex.hasSum_conj' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x)) (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f x)
-but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x)) (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f x)
-Case conversion may be inaccurate. Consider using '#align complex.has_sum_conj' Complex.hasSum_conj'ₓ'. -/
 theorem hasSum_conj' {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   IsROrC.hasSum_conj' _
 #align complex.has_sum_conj' Complex.hasSum_conj'
 
-/- warning: complex.summable_conj -> Complex.summable_conj is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {f : α -> Complex}, Iff (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x))) (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align complex.summable_conj Complex.summable_conjₓ'. -/
 @[simp]
 theorem summable_conj {f : α → ℂ} : (Summable fun x => conj (f x)) ↔ Summable f :=
   IsROrC.summable_conj _
 #align complex.summable_conj Complex.summable_conj
 
-/- warning: complex.conj_tsum -> Complex.conj_tsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.conj_tsum Complex.conj_tsumₓ'. -/
 theorem conj_tsum (f : α → ℂ) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   IsROrC.conj_tsum _
 #align complex.conj_tsum Complex.conj_tsum
 
-/- warning: complex.has_sum_of_real -> Complex.hasSum_ofReal is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Real} {x : Real}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => Complex.ofReal' (f x)) (Complex.ofReal' x)) (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x)
-Case conversion may be inaccurate. Consider using '#align complex.has_sum_of_real Complex.hasSum_ofRealₓ'. -/
 @[simp, norm_cast]
 theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : ℂ)) x ↔ HasSum f x :=
   IsROrC.hasSum_ofReal _
 #align complex.has_sum_of_real Complex.hasSum_ofReal
 
-/- warning: complex.summable_of_real -> Complex.summable_ofReal is a dubious translation:
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-  forall {α : Type.{u1}} {f : α -> Real}, Iff (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => Complex.ofReal' (f x))) (Summable.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f)
-Case conversion may be inaccurate. Consider using '#align complex.summable_of_real Complex.summable_ofRealₓ'. -/
 @[simp, norm_cast]
 theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : ℂ)) ↔ Summable f :=
   IsROrC.summable_ofReal _
 #align complex.summable_of_real Complex.summable_ofReal
 
-/- warning: complex.of_real_tsum -> Complex.ofReal_tsum is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {α : Type.{u1}} (f : α -> Real), Eq.{1} Complex (Complex.ofReal' (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => Complex.ofReal' (f a)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_tsum Complex.ofReal_tsumₓ'. -/
 @[norm_cast]
 theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : ℂ) = ∑' a, f a :=
   IsROrC.ofReal_tsum _ _
 #align complex.of_real_tsum Complex.ofReal_tsum
 
-/- warning: complex.has_sum_re -> Complex.hasSum_re is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f x) -> (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.re (f x)) (Complex.re x))
-Case conversion may be inaccurate. Consider using '#align complex.has_sum_re Complex.hasSum_reₓ'. -/
 theorem hasSum_re {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).re) x.re :=
   IsROrC.hasSum_re _ h
 #align complex.has_sum_re Complex.hasSum_re
 
-/- warning: complex.has_sum_im -> Complex.hasSum_im is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align complex.has_sum_im Complex.hasSum_imₓ'. -/
 theorem hasSum_im {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).im) x.im :=
   IsROrC.hasSum_im _ h
 #align complex.has_sum_im Complex.hasSum_im
 
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-but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Complex}, (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f) -> (Eq.{1} Real (Complex.re (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => Complex.re (f a))))
-Case conversion may be inaccurate. Consider using '#align complex.re_tsum Complex.re_tsumₓ'. -/
 theorem re_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).re = ∑' a, (f a).re :=
   IsROrC.re_tsum _ h
 #align complex.re_tsum Complex.re_tsum
 
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-but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Complex}, (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f) -> (Eq.{1} Real (Complex.im (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => Complex.im (f a))))
-Case conversion may be inaccurate. Consider using '#align complex.im_tsum Complex.im_tsumₓ'. -/
 theorem im_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).im = ∑' a, (f a).im :=
   IsROrC.im_tsum _ h
 #align complex.im_tsum Complex.im_tsum
 
-/- warning: complex.has_sum_iff -> Complex.hasSum_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (f : α -> Complex) (c : Complex), Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f c) (And (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.re (f x)) (Complex.re c)) (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.im (f x)) (Complex.im c)))
-but is expected to have type
-  forall {α : Type.{u1}} (f : α -> Complex) (c : Complex), Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f c) (And (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.re (f x)) (Complex.re c)) (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.im (f x)) (Complex.im c)))
-Case conversion may be inaccurate. Consider using '#align complex.has_sum_iff Complex.hasSum_iffₓ'. -/
 theorem hasSum_iff (f : α → ℂ) (c : ℂ) :
     HasSum f c ↔ HasSum (fun x => (f x).re) c.re ∧ HasSum (fun x => (f x).im) c.im :=
   IsROrC.hasSum_iff _ _

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

@@ -132,10 +132,8 @@ lean 3 declaration is
 but is expected to have type
   forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w) (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Complex.re z) (Complex.re w)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Complex.im z) (Complex.im w)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
 Case conversion may be inaccurate. Consider using '#align complex.dist_eq_re_im Complex.dist_eq_re_imₓ'. -/
-theorem dist_eq_re_im (z w : ℂ) : dist z w = Real.sqrt ((z.re - w.re) ^ 2 + (z.im - w.im) ^ 2) :=
-  by
-  rw [sq, sq]
-  rfl
+theorem dist_eq_re_im (z w : ℂ) : dist z w = Real.sqrt ((z.re - w.re) ^ 2 + (z.im - w.im) ^ 2) := by
+  rw [sq, sq]; rfl
 #align complex.dist_eq_re_im Complex.dist_eq_re_im
 
 /- warning: complex.dist_mk -> Complex.dist_mk is a dubious translation:
@@ -278,10 +276,7 @@ but is expected to have type
   forall (r : Rat), Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Rat.cast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Rat.cast.{0} Real Real.ratCast r))
 Case conversion may be inaccurate. Consider using '#align complex.norm_rat Complex.norm_ratₓ'. -/
 @[simp]
-theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| :=
-  by
-  rw [← of_real_rat_cast]
-  exact norm_real _
+theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| := by rw [← of_real_rat_cast]; exact norm_real _
 #align complex.norm_rat Complex.norm_rat
 
 /- warning: complex.norm_nat -> Complex.norm_nat is a dubious translation:
@@ -559,20 +554,15 @@ Case conversion may be inaccurate. Consider using '#align complex.restrict_scala
 theorem restrictScalars_one_smulRight' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =
       reClm.smul_right x + I • imClm.smul_right x :=
-  by
-  ext ⟨a, b⟩
-  simp [mk_eq_add_mul_I, add_smul, mul_smul, smul_comm I]
+  by ext ⟨a, b⟩; simp [mk_eq_add_mul_I, add_smul, mul_smul, smul_comm I]
 #align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'
 
 /- warning: complex.restrict_scalars_one_smul_right -> Complex.restrictScalars_one_smulRight is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRightₓ'. -/
 theorem restrictScalars_one_smulRight (x : ℂ) :
-    ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] ℂ) = x • 1 :=
-  by
-  ext1 z
-  dsimp
-  apply mul_comm
+    ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] ℂ) = x • 1 := by
+  ext1 z; dsimp; apply mul_comm
 #align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRight
 
 /- warning: complex.conj_lie -> Complex.conjLie is a dubious translation:

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

@@ -505,10 +505,7 @@ theorem reClm_coe : (coe reClm : ℂ →ₗ[ℝ] ℝ) = reLm :=
 #align complex.re_clm_coe Complex.reClm_coe
 
 /- warning: complex.re_clm_apply -> Complex.reClm_apply is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (fun (_x : ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) => Complex -> Real) (ContinuousLinearMap.toFun.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) Complex.reClm z) (Complex.re z)
-but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Real) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) Complex.reClm z) (Complex.re z)
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.re_clm_apply Complex.reClm_applyₓ'. -/
 @[simp]
 theorem reClm_apply (z : ℂ) : (reClm : ℂ → ℝ) z = z.re :=
@@ -549,35 +546,26 @@ theorem imClm_coe : (coe imClm : ℂ →ₗ[ℝ] ℝ) = imLm :=
 #align complex.im_clm_coe Complex.imClm_coe
 
 /- warning: complex.im_clm_apply -> Complex.imClm_apply is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (fun (_x : ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) => Complex -> Real) (ContinuousLinearMap.toFun.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) Complex.imClm z) (Complex.im z)
-but is expected to have type
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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Real) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} 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(PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) Complex.imClm z) (Complex.im z)
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.im_clm_apply Complex.imClm_applyₓ'. -/
 @[simp]
 theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
   rfl
 #align complex.im_clm_apply Complex.imClm_apply
 
-/- warning: complex.restrict_scalars_one_smul_right' -> Complex.restrictScalars_one_smul_right' is a dubious translation:
-lean 3 declaration is
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(UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.ring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LinearMap.IsScalarTower.compatibleSMul.{0, u1, 0, 0} Complex E (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Complex (Ring.toSemiring.{0} Complex 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(AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (Module.real_complex_tower.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} 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_inst_1 _inst_2))) (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E 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Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.reClm x) (SMul.smul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (SMulZeroClass.toHasSmul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Ring.toSemiring.{0} Complex Complex.ring) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (ContinuousLinearMap.module.{0, 0, 0, 0, u1} Real Real Complex (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Complex Complex.ring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulCommClass.complexToReal.{0, u1} Complex E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Complex (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) Real.module (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E Real.monoid (MulActionWithZero.toMulAction.{0, u1} Real E Real.monoidWithZero (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
-but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.instRingReal) (Ring.toSemiring.{0} Real Real.instRingReal) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real 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(NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 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(ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex 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Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (SMulZeroClass.toSMul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.zero.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Module.toMulActionWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.instSemiringComplex (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex 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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (ContinuousLinearMap.module.{0, 0, 0, 0, u1} Real Real 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(NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulCommClass.complexToReal.{0, u1} Complex E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulZeroClass.toSMul.{0, u1} Complex E 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex 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(SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring 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(Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
-Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smul_right'ₓ'. -/
-theorem restrictScalars_one_smul_right' (x : E) :
+/- warning: complex.restrict_scalars_one_smul_right' -> Complex.restrictScalars_one_smulRight' is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'ₓ'. -/
+theorem restrictScalars_one_smulRight' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =
       reClm.smul_right x + I • imClm.smul_right x :=
   by
   ext ⟨a, b⟩
   simp [mk_eq_add_mul_I, add_smul, mul_smul, smul_comm I]
-#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smul_right'
+#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'
 
 /- warning: complex.restrict_scalars_one_smul_right -> Complex.restrictScalars_one_smulRight is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRightₓ'. -/
 theorem restrictScalars_one_smulRight (x : ℂ) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] ℂ) = x • 1 :=
@@ -599,10 +587,7 @@ def conjLie : ℂ ≃ₗᵢ[ℝ] ℂ :=
 #align complex.conj_lie Complex.conjLie
 
 /- warning: complex.conj_lie_apply -> Complex.conjLie_apply is a dubious translation:
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Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.conj_lie_apply Complex.conjLie_applyₓ'. -/
 @[simp]
 theorem conjLie_apply (z : ℂ) : conjLie z = conj z :=
@@ -725,10 +710,7 @@ theorem conjCle_coe : conjCle.toLinearEquiv = conjAe.toLinearEquiv :=
 #align complex.conj_cle_coe Complex.conjCle_coe
 
 /- warning: complex.conj_cle_apply -> Complex.conjCle_apply is a dubious translation:
-lean 3 declaration is
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(RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.conj_cle_apply Complex.conjCle_applyₓ'. -/
 @[simp]
 theorem conjCle_apply (z : ℂ) : conjCle z = conj z :=
@@ -804,10 +786,7 @@ theorem ofRealClm_coe : (ofRealClm : ℝ →ₗ[ℝ] ℂ) = ofRealAm.toLinearMap
 #align complex.of_real_clm_coe Complex.ofRealClm_coe
 
 /- warning: complex.of_real_clm_apply -> Complex.ofRealClm_apply is a dubious translation:
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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))) Complex.ofRealClm x) (Complex.ofReal' x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.of_real_clm_apply Complex.ofRealClm_applyₓ'. -/
 @[simp]
 theorem ofRealClm_apply (x : ℝ) : ofRealClm x = x :=
@@ -943,10 +922,7 @@ section tsum
 variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]
 
 /- warning: is_R_or_C.has_sum_conj -> IsROrC.hasSum_conj is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) x) (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x))
-but is expected to have type
-  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) x) (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_conj IsROrC.hasSum_conjₓ'. -/
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
@@ -954,10 +930,7 @@ theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x))
 #align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
 
 /- warning: is_R_or_C.has_sum_conj' -> IsROrC.hasSum_conj' is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x)) (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'ₓ'. -/
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   conjCle.hasSum'
@@ -977,10 +950,7 @@ theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Sum
 variable {𝕜}
 
 /- warning: is_R_or_C.conj_tsum -> IsROrC.conj_tsum is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : IsROrC.{u2} 𝕜] (f : α -> 𝕜), Eq.{succ u2} 𝕜 (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (tsum.{u2, u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{u2, u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f a)))
-but is expected to have type
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(Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) 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(DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_tsum IsROrC.conj_tsumₓ'. -/
 theorem conj_tsum (f : α → 𝕜) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   tsum_star
@@ -1017,40 +987,28 @@ theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, f a :
 -/
 
 /- warning: is_R_or_C.has_sum_re -> IsROrC.hasSum_re is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_re IsROrC.hasSum_reₓ'. -/
 theorem hasSum_re {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => re (f x)) (re x) :=
   reClm.HasSum h
 #align is_R_or_C.has_sum_re IsROrC.hasSum_re
 
 /- warning: is_R_or_C.has_sum_im -> IsROrC.hasSum_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_im IsROrC.hasSum_imₓ'. -/
 theorem hasSum_im {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => im (f x)) (im x) :=
   imClm.HasSum h
 #align is_R_or_C.has_sum_im IsROrC.hasSum_im
 
 /- warning: is_R_or_C.re_tsum -> IsROrC.re_tsum is a dubious translation:
-lean 3 declaration is
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_inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 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(DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) (f a))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_tsum IsROrC.re_tsumₓ'. -/
 theorem re_tsum {f : α → 𝕜} (h : Summable f) : re (∑' a, f a) = ∑' a, re (f a) :=
   reClm.map_tsum h
 #align is_R_or_C.re_tsum IsROrC.re_tsum
 
 /- warning: is_R_or_C.im_tsum -> IsROrC.im_tsum is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_tsum IsROrC.im_tsumₓ'. -/
 theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a, im (f a) :=
   imClm.map_tsum h
@@ -1059,10 +1017,7 @@ theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a,
 variable {𝕜}
 
 /- warning: is_R_or_C.has_sum_iff -> IsROrC.hasSum_iff is a dubious translation:
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-but is expected to have type
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(fun (x : α) => FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) (f x)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) c)) (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u2} 𝕜 _inst_1) (f x)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u2} 𝕜 _inst_1) c)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_iff IsROrC.hasSum_iffₓ'. -/
 theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
     HasSum f c ↔ HasSum (fun x => re (f x)) (re c) ∧ HasSum (fun x => im (f x)) (im c) :=
@@ -1128,10 +1083,7 @@ theorem summable_conj {f : α → ℂ} : (Summable fun x => conj (f x)) ↔ Summ
 #align complex.summable_conj Complex.summable_conj
 
 /- warning: complex.conj_tsum -> Complex.conj_tsum is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {α : Type.{u1}} (f : α -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) 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Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex 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(NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex 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(CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.conj_tsum Complex.conj_tsumₓ'. -/
 theorem conj_tsum (f : α → ℂ) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   IsROrC.conj_tsum _

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -563,7 +563,7 @@ theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.restrictScalars.{0, 0, u1, 0} Complex Complex E Complex.ring Complex.addCommGroup (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.ring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LinearMap.IsScalarTower.compatibleSMul.{0, u1, 0, 0} Complex E (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Complex (Ring.toSemiring.{0} Complex Complex.ring) (Complex.hasSmul.{0} Real (Mul.toSMul.{0} Real Real.hasMul)) (SMulZeroClass.toHasSmul.{0, 0} Real Complex (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (SMulWithZero.toSmulZeroClass.{0, 0} Real Complex (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring))))) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring)) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (Module.toMulActionWithZero.{0, 0} Real Complex (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (Module.real_complex_tower.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Complex Complex (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (IsScalarTower.left.{0, u1} Complex E (Ring.toMonoid.{0} Complex Complex.ring) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E 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Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.reClm x) (SMul.smul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (SMulZeroClass.toHasSmul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Ring.toSemiring.{0} Complex Complex.ring) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (ContinuousLinearMap.module.{0, 0, 0, 0, u1} Real Real Complex (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Complex Complex.ring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulCommClass.complexToReal.{0, u1} Complex E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Complex (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) Real.module (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E Real.monoid (MulActionWithZero.toMulAction.{0, u1} Real E Real.monoidWithZero (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.instRingReal) (Ring.toSemiring.{0} Real Real.instRingReal) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.restrictScalars.{0, 0, u1, 0} Complex Complex E Complex.instRingComplex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.instRingReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real 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(NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 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(ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex 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Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (SMulZeroClass.toSMul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.zero.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex 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(Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) 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(SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Module.toMulActionWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.instSemiringComplex (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (ContinuousLinearMap.module.{0, 0, 0, 0, u1} Real Real 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(NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulCommClass.complexToReal.{0, u1} Complex E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulZeroClass.toSMul.{0, u1} Complex E 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex 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(SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (MulActionWithZero.toMulAction.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.instRingReal) (Ring.toSemiring.{0} Real Real.instRingReal) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.restrictScalars.{0, 0, u1, 0} Complex Complex E Complex.instRingComplex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.instRingReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LinearMap.IsScalarTower.compatibleSMul.{0, u1, 0, 0} Complex E (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) Real Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) (Complex.instSMulComplex.{0} Real (Algebra.toSMul.{0, 0} Real Real Real.instCommSemiringReal Real.semiring (NormedAlgebra.toAlgebra.{0, 0} Real Real Real.normedField (SeminormedCommRing.toSeminormedRing.{0} Real (NormedCommRing.toSeminormedCommRing.{0} Real Real.normedCommRing)) (IsROrC.toNormedAlgebra.{0} Real Real.isROrC)))) (SMulZeroClass.toSMul.{0, 0} Real Complex (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (SMulWithZero.toSMulZeroClass.{0, 0} Real Complex (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal)) (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (Module.toMulActionWithZero.{0, 0} Real Complex (Ring.toSemiring.{0} Real Real.instRingReal) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal)) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real Real.instRingReal) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (Module.real_complex_tower.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (IsScalarTower.left.{0, u1} Complex E (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) 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Complex.instNormedFieldComplex)))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex 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(Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.instZeroComplex (ContinuousLinearMap.zero.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (ContinuousLinearMap.zero.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Module.toMulActionWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.instSemiringComplex (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex 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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (ContinuousLinearMap.module.{0, 0, 0, 0, u1} Real Real Complex Real.semiring Real.semiring Complex.instSemiringComplex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulCommClass.complexToReal.{0, u1} Complex E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (MulActionWithZero.toMulAction.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
 Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smul_right'ₓ'. -/
 theorem restrictScalars_one_smul_right' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =

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

@@ -214,7 +214,7 @@ theorem edist_of_im_eq {z w : ℂ} (h : z.im = w.im) : edist z w = edist z.re w.
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
+  forall (z : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.dist_conj_self Complex.dist_conj_selfₓ'. -/
 theorem dist_conj_self (z : ℂ) : dist (conj z) z = 2 * |z.im| := by
   rw [dist_of_re_eq (conj_re z), conj_im, dist_comm, Real.dist_eq, sub_neg_eq_add, ← two_mul,
@@ -225,7 +225,7 @@ theorem dist_conj_self (z : ℂ) : dist (conj z) z = 2 * |z.im| := by
 lean 3 declaration is
   forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (HMul.hMul.{0, 0, 0} NNReal ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) (Complex.im z)) NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Complex.im z)))
+  forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (HMul.hMul.{0, 0, 0} NNReal ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) (Complex.im z)) NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_self Complex.nndist_conj_selfₓ'. -/
 theorem nndist_conj_self (z : ℂ) : nndist (conj z) z = 2 * Real.nnabs z.im :=
   NNReal.eq <| by rw [← dist_nndist, NNReal.coe_mul, NNReal.coe_two, Real.coe_nnabs, dist_conj_self]
@@ -235,7 +235,7 @@ theorem nndist_conj_self (z : ℂ) : nndist (conj z) z = 2 * Real.nnabs z.im :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
+  forall (z : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.dist_self_conj Complex.dist_self_conjₓ'. -/
 theorem dist_self_conj (z : ℂ) : dist z (conj z) = 2 * |z.im| := by rw [dist_comm, dist_conj_self]
 #align complex.dist_self_conj Complex.dist_self_conj
@@ -244,7 +244,7 @@ theorem dist_self_conj (z : ℂ) : dist z (conj z) = 2 * |z.im| := by rw [dist_c
 lean 3 declaration is
   forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} NNReal ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) (Complex.im z)) NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Complex.im z)))
+  forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} NNReal ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) (Complex.im z)) NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.nndist_self_conj Complex.nndist_self_conjₓ'. -/
 theorem nndist_self_conj (z : ℂ) : nndist z (conj z) = 2 * Real.nnabs z.im := by
   rw [nndist_comm, nndist_conj_self]
@@ -330,7 +330,7 @@ theorem continuous_abs : Continuous abs :=
 lean 3 declaration is
   Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq)
 but is expected to have type
-  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq)
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq)
 Case conversion may be inaccurate. Consider using '#align complex.continuous_norm_sq Complex.continuous_normSqₓ'. -/
 @[continuity]
 theorem continuous_normSq : Continuous normSq := by
@@ -396,7 +396,7 @@ theorem norm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Norm.norm.{0} (Prod.{0, 0} Real Real) (Prod.hasNorm.{0, 0} Real Real Real.hasNorm Real.hasNorm) (coeFn.{1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) (fun (_x : Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) => Complex -> (Prod.{0, 0} Real Real)) (Equiv.hasCoeToFun.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) z) (Prod.toNorm.{0, 0} Real Real Real.norm Real.norm) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Complex) => Prod.{0, 0} Real Real) z) (Prod.toNorm.{0, 0} Real Real Real.norm Real.norm) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_apply_le Complex.equivRealProd_apply_leₓ'. -/
 theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ abs z := by
   simp [Prod.norm_def, abs_re_le_abs, abs_im_le_abs]
@@ -406,7 +406,7 @@ theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ abs z := by
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Norm.norm.{0} (Prod.{0, 0} Real Real) (Prod.hasNorm.{0, 0} Real Real Real.hasNorm Real.hasNorm) (coeFn.{1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) (fun (_x : Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) => Complex -> (Prod.{0, 0} Real Real)) (Equiv.hasCoeToFun.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) z) (Prod.toNorm.{0, 0} Real Real Real.norm Real.norm) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd z)) (HMul.hMul.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z))
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Complex) => Prod.{0, 0} Real Real) z) (Prod.toNorm.{0, 0} Real Real Real.norm Real.norm) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd z)) (HMul.hMul.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z))
 Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_apply_le' Complex.equivRealProd_apply_le'ₓ'. -/
 theorem equivRealProd_apply_le' (z : ℂ) : ‖equivRealProd z‖ ≤ 1 * abs z := by
   simpa using equiv_real_prod_apply_le z
@@ -428,7 +428,7 @@ theorem antilipschitz_equivRealProd : AntilipschitzWith (NNReal.sqrt 2) equivRea
 lean 3 declaration is
   UniformEmbedding.{0, 0} Complex (Prod.{0, 0} Real Real) (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Prod.uniformSpace.{0, 0} Real Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) (fun (_x : Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) => Complex -> (Prod.{0, 0} Real Real)) (Equiv.hasCoeToFun.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd)
 but is expected to have type
-  UniformEmbedding.{0, 0} Complex (Prod.{0, 0} Real Real) (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (instUniformSpaceProd.{0, 0} Real Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd)
+  UniformEmbedding.{0, 0} Complex (Prod.{0, 0} Real Real) (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (instUniformSpaceProd.{0, 0} Real Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd)
 Case conversion may be inaccurate. Consider using '#align complex.uniform_embedding_equiv_real_prod Complex.uniformEmbedding_equivRealProdₓ'. -/
 theorem uniformEmbedding_equivRealProd : UniformEmbedding equivRealProd :=
   antilipschitz_equivRealProd.UniformEmbedding lipschitz_equivRealProd.UniformContinuous
@@ -602,7 +602,7 @@ def conjLie : ℂ ≃ₗᵢ[ℝ] ℂ :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (fun (_x : LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) => Complex -> Complex) (LinearIsometryEquiv.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) Complex.conjLie z) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField 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Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) Complex.conjLie z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) Complex.conjLie z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)
 Case conversion may be inaccurate. Consider using '#align complex.conj_lie_apply Complex.conjLie_applyₓ'. -/
 @[simp]
 theorem conjLie_apply (z : ℂ) : conjLie z = conj z :=
@@ -624,7 +624,7 @@ theorem conjLie_symm : conjLie.symm = conjLie :=
 lean 3 declaration is
   Isometry.{0, 0} Complex Complex (PseudoMetricSpace.toPseudoEMetricSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (PseudoMetricSpace.toPseudoEMetricSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing))
 but is expected to have type
-  Isometry.{0, 0} Complex Complex (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex))) (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
+  Isometry.{0, 0} Complex Complex (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex))) (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
 Case conversion may be inaccurate. Consider using '#align complex.isometry_conj Complex.isometry_conjₓ'. -/
 theorem isometry_conj : Isometry (conj : ℂ → ℂ) :=
   conjLie.Isometry
@@ -634,7 +634,7 @@ theorem isometry_conj : Isometry (conj : ℂ → ℂ) :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)) (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w)
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)) (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w)
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)) (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w)
 Case conversion may be inaccurate. Consider using '#align complex.dist_conj_conj Complex.dist_conj_conjₓ'. -/
 @[simp]
 theorem dist_conj_conj (z w : ℂ) : dist (conj z) (conj w) = dist z w :=
@@ -645,7 +645,7 @@ theorem dist_conj_conj (z w : ℂ) : dist (conj z) (conj w) = dist z w :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w)
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w)
+  forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w)
 Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_conj Complex.nndist_conj_conjₓ'. -/
 @[simp]
 theorem nndist_conj_conj (z w : ℂ) : nndist (conj z) (conj w) = nndist z w :=
@@ -656,7 +656,7 @@ theorem nndist_conj_conj (z w : ℂ) : nndist (conj z) (conj w) = nndist z w :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) w) (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) w) (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w))
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) w) (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w))
 Case conversion may be inaccurate. Consider using '#align complex.dist_conj_comm Complex.dist_conj_commₓ'. -/
 theorem dist_conj_comm (z w : ℂ) : dist (conj z) w = dist z (conj w) := by
   rw [← dist_conj_conj, conj_conj]
@@ -666,7 +666,7 @@ theorem dist_conj_comm (z w : ℂ) : dist (conj z) w = dist z (conj w) := by
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) w) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) w) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w))
+  forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) w) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w))
 Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_comm Complex.nndist_conj_commₓ'. -/
 theorem nndist_conj_comm (z w : ℂ) : nndist (conj z) w = nndist z (conj w) :=
   Subtype.ext <| dist_conj_comm _ _
@@ -679,7 +679,7 @@ instance : ContinuousStar ℂ :=
 lean 3 declaration is
   Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing))
 but is expected to have type
-  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
 Case conversion may be inaccurate. Consider using '#align complex.continuous_conj Complex.continuous_conjₓ'. -/
 @[continuity]
 theorem continuous_conj : Continuous (conj : ℂ → ℂ) :=
@@ -690,7 +690,7 @@ theorem continuous_conj : Continuous (conj : ℂ → ℂ) :=
 lean 3 declaration is
   forall {f : RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))}, (Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f)) -> (Or (Eq.{1} (RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f (RingHom.id.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) (Eq.{1} (RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing)))
 but is expected to have type
-  forall {f : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)}, (Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) f)) -> (Or (Eq.{1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (Eq.{1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing)))
+  forall {f : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)}, (Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) f)) -> (Or (Eq.{1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (Eq.{1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing)))
 Case conversion may be inaccurate. Consider using '#align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuousₓ'. -/
 /-- The only continuous ring homomorphisms from `ℂ` to `ℂ` are the identity and the complex
 conjugation. -/
@@ -728,7 +728,7 @@ theorem conjCle_coe : conjCle.toLinearEquiv = conjAe.toLinearEquiv :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (fun (_x : ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) => Complex -> Complex) (ContinuousLinearEquiv.hasCoeToFun.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) Complex.conjCle z) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex 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(NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real 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(RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex 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Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{0, 0, 0, 0, 0} (ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) Complex.conjCle z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)
 Case conversion may be inaccurate. Consider using '#align complex.conj_cle_apply Complex.conjCle_applyₓ'. -/
 @[simp]
 theorem conjCle_apply (z : ℂ) : conjCle z = conj z :=
@@ -771,7 +771,7 @@ theorem continuous_ofReal : Continuous (coe : ℝ → ℂ) :=
 lean 3 declaration is
   forall {f : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))}, (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (coeFn.{1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Real -> Complex) (RingHom.hasCoeToFun.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f)) -> (Eq.{1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f Complex.ofReal)
 but is expected to have type
-  forall {f : RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)}, (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) f)) -> (Eq.{1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f Complex.ofReal)
+  forall {f : RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)}, (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) f)) -> (Eq.{1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f Complex.ofReal)
 Case conversion may be inaccurate. Consider using '#align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuousₓ'. -/
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
 theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) : f = Complex.ofReal :=
@@ -931,7 +931,7 @@ theorem I_to_complex : IC = Complex.I :=
 lean 3 declaration is
   forall {x : Complex}, Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{0} Complex Complex.isROrC) x) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x)
 but is expected to have type
-  forall {x : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{0} Complex Complex.instIsROrCComplex) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq x)
+  forall {x : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{0} Complex Complex.instIsROrCComplex) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq x)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complexₓ'. -/
 @[simp]
 theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x :=
@@ -946,7 +946,7 @@ variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]
 lean 3 declaration is
   forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) x) (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x))
 but is expected to have type
-  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) x) (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x))
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) x) (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_conj IsROrC.hasSum_conjₓ'. -/
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
@@ -957,7 +957,7 @@ theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x))
 lean 3 declaration is
   forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x)) (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x)
 but is expected to have type
-  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x)) (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x)
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x)) (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'ₓ'. -/
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   conjCle.hasSum'
@@ -967,7 +967,7 @@ theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x))
 lean 3 declaration is
   forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, Iff (Summable.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x))) (Summable.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f)
 but is expected to have type
-  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, Iff (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x))) (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f)
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, Iff (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x))) (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.summable_conj IsROrC.summable_conjₓ'. -/
 @[simp]
 theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Summable f :=
@@ -980,7 +980,7 @@ variable {𝕜}
 lean 3 declaration is
   forall {α : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : IsROrC.{u2} 𝕜] (f : α -> 𝕜), Eq.{succ u2} 𝕜 (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (tsum.{u2, u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{u2, u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : IsROrC.{u2} 𝕜] (f : α -> 𝕜), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f a)))
+  forall {α : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : IsROrC.{u2} 𝕜] (f : α -> 𝕜), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f a)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_tsum IsROrC.conj_tsumₓ'. -/
 theorem conj_tsum (f : α → 𝕜) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   tsum_star
@@ -1099,7 +1099,7 @@ open ComplexConjugate
 lean 3 declaration is
   forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x)) x) (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x))
 but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x)) x) (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x))
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x)) x) (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x))
 Case conversion may be inaccurate. Consider using '#align complex.has_sum_conj Complex.hasSum_conjₓ'. -/
 @[simp]
 theorem hasSum_conj {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
@@ -1110,7 +1110,7 @@ theorem hasSum_conj {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) x
 lean 3 declaration is
   forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x)) (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f x)
 but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x)) (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f x)
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x)) (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f x)
 Case conversion may be inaccurate. Consider using '#align complex.has_sum_conj' Complex.hasSum_conj'ₓ'. -/
 theorem hasSum_conj' {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   IsROrC.hasSum_conj' _
@@ -1120,7 +1120,7 @@ theorem hasSum_conj' {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) (
 lean 3 declaration is
   forall {α : Type.{u1}} {f : α -> Complex}, Iff (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x))) (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f)
 but is expected to have type
-  forall {α : Type.{u1}} {f : α -> Complex}, Iff (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x))) (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f)
+  forall {α : Type.{u1}} {f : α -> Complex}, Iff (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x))) (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f)
 Case conversion may be inaccurate. Consider using '#align complex.summable_conj Complex.summable_conjₓ'. -/
 @[simp]
 theorem summable_conj {f : α → ℂ} : (Summable fun x => conj (f x)) ↔ Summable f :=
@@ -1131,7 +1131,7 @@ theorem summable_conj {f : α → ℂ} : (Summable fun x => conj (f x)) ↔ Summ
 lean 3 declaration is
   forall {α : Type.{u1}} (f : α -> Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (tsum.{0, u1} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) α (fun (a : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f a)))
 but is expected to have type
-  forall {α : Type.{u1}} (f : α -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f a)))
+  forall {α : Type.{u1}} (f : α -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f a)))
 Case conversion may be inaccurate. Consider using '#align complex.conj_tsum Complex.conj_tsumₓ'. -/
 theorem conj_tsum (f : α → ℂ) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   IsROrC.conj_tsum _

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.complex.basic
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
+! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Topology.Instances.RealVectorSpace
 /-!
 # Normed space structure on `ℂ`.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file gathers basic facts on complex numbers of an analytic nature.
 
 ## Main results

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

@@ -863,7 +863,7 @@ open ComplexOrder
 
 /- warning: complex.eq_coe_norm_of_nonneg -> Complex.eq_coe_norm_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Norm.norm.{0} Complex Complex.hasNorm z)))
+  forall {z : Complex}, (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Norm.norm.{0} Complex Complex.hasNorm z)))
 but is expected to have type
   forall {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) z) -> (Eq.{1} Complex z (Complex.ofReal' (Norm.norm.{0} Complex Complex.instNormComplex z)))
 Case conversion may be inaccurate. Consider using '#align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonnegₓ'. -/

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

@@ -560,7 +560,7 @@ theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.restrictScalars.{0, 0, u1, 0} Complex Complex E Complex.ring Complex.addCommGroup (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.ring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LinearMap.IsScalarTower.compatibleSMul.{0, u1, 0, 0} Complex E (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Complex (Ring.toSemiring.{0} Complex Complex.ring) (Complex.hasSmul.{0} Real (Mul.toSMul.{0} Real Real.hasMul)) (SMulZeroClass.toHasSmul.{0, 0} Real Complex (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (SMulWithZero.toSmulZeroClass.{0, 0} Real Complex (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring))))) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring)) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (Module.toMulActionWithZero.{0, 0} Real Complex (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (Module.real_complex_tower.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} 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(SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) Real.module (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E Real.monoid (MulActionWithZero.toMulAction.{0, u1} Real E Real.monoidWithZero (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.reClm x) (SMul.smul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (SMulZeroClass.toHasSmul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Ring.toSemiring.{0} Complex Complex.ring) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (ContinuousLinearMap.module.{0, 0, 0, 0, u1} Real Real Complex (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Complex Complex.ring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulCommClass.complexToReal.{0, u1} Complex E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Complex (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) Real.module (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E Real.monoid (MulActionWithZero.toMulAction.{0, u1} Real E Real.monoidWithZero (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.instRingReal) (Ring.toSemiring.{0} Real Real.instRingReal) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.restrictScalars.{0, 0, u1, 0} Complex Complex E Complex.instRingComplex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.instRingReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LinearMap.IsScalarTower.compatibleSMul.{0, u1, 0, 0} Complex E (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) Real Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) (Complex.instSMulComplex.{0} Real (Algebra.toSMul.{0, 0} Real Real Real.instCommSemiringReal Real.semiring (NormedAlgebra.toAlgebra.{0, 0} Real Real Real.normedField (SeminormedCommRing.toSeminormedRing.{0} Real (NormedCommRing.toSeminormedCommRing.{0} Real Real.normedCommRing)) (IsROrC.toNormedAlgebra.{0} Real Real.isROrC)))) (SMulZeroClass.toSMul.{0, 0} Real Complex (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (SMulWithZero.toSMulZeroClass.{0, 0} Real Complex (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} 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(NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} 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(SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (Module.real_complex_tower.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (IsScalarTower.left.{0, u1} Complex E (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)) (OfNat.ofNat.{0} (ContinuousLinearMap.{0, 0, 0, 0} Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex))) 1 (One.toOfNat1.{0} (ContinuousLinearMap.{0, 0, 0, 0} Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex 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(NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.add.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E 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(AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex 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Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (MulActionWithZero.toMulAction.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.instRingReal) (Ring.toSemiring.{0} Real Real.instRingReal) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.restrictScalars.{0, 0, u1, 0} Complex Complex E Complex.instRingComplex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.instRingReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LinearMap.IsScalarTower.compatibleSMul.{0, u1, 0, 0} Complex E (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) Real Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) (Complex.instSMulComplex.{0} Real (Algebra.toSMul.{0, 0} Real Real Real.instCommSemiringReal Real.semiring (NormedAlgebra.toAlgebra.{0, 0} Real Real Real.normedField (SeminormedCommRing.toSeminormedRing.{0} Real (NormedCommRing.toSeminormedCommRing.{0} Real Real.normedCommRing)) (IsROrC.toNormedAlgebra.{0} Real Real.isROrC)))) (SMulZeroClass.toSMul.{0, 0} Real Complex (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (SMulWithZero.toSMulZeroClass.{0, 0} Real Complex (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal)) (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (Module.toMulActionWithZero.{0, 0} Real Complex (Ring.toSemiring.{0} Real Real.instRingReal) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal)) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real Real.instRingReal) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (Module.real_complex_tower.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex 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(Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.instZeroComplex (ContinuousLinearMap.zero.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Module.toMulActionWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.instSemiringComplex (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (ContinuousLinearMap.module.{0, 0, 0, 0, u1} Real Real Complex Real.semiring Real.semiring Complex.instSemiringComplex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulCommClass.complexToReal.{0, u1} Complex E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (MulActionWithZero.toMulAction.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
 Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smul_right'ₓ'. -/
 theorem restrictScalars_one_smul_right' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =

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

@@ -49,14 +49,26 @@ open ComplexConjugate Topology
 instance : Norm ℂ :=
   ⟨abs⟩
 
+/- warning: complex.norm_eq_abs -> Complex.norm_eq_abs is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
+Case conversion may be inaccurate. Consider using '#align complex.norm_eq_abs Complex.norm_eq_absₓ'. -/
 @[simp]
 theorem norm_eq_abs (z : ℂ) : ‖z‖ = abs z :=
   rfl
 #align complex.norm_eq_abs Complex.norm_eq_abs
 
-theorem norm_exp_of_real_mul_i (t : ℝ) : ‖exp (t * I)‖ = 1 := by
+/- warning: complex.norm_exp_of_real_mul_I -> Complex.norm_exp_ofReal_mul_I is a dubious translation:
+lean 3 declaration is
+  forall (t : Real), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) t) Complex.I))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall (t : Real), Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' t) Complex.I))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align complex.norm_exp_of_real_mul_I Complex.norm_exp_ofReal_mul_Iₓ'. -/
+theorem norm_exp_ofReal_mul_I (t : ℝ) : ‖exp (t * I)‖ = 1 := by
   simp only [norm_eq_abs, abs_exp_of_real_mul_I]
-#align complex.norm_exp_of_real_mul_I Complex.norm_exp_of_real_mul_i
+#align complex.norm_exp_of_real_mul_I Complex.norm_exp_ofReal_mul_I
 
 instance : NormedAddCommGroup ℂ :=
   AddGroupNorm.toNormedAddCommGroup
@@ -89,77 +101,179 @@ instance {R : Type _} [NormedField R] [NormedAlgebra R ℝ] : NormedAlgebra R 
 
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
+/- warning: normed_space.complex_to_real -> NormedSpace.complexToReal is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)], NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)], NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)
+Case conversion may be inaccurate. Consider using '#align normed_space.complex_to_real NormedSpace.complexToRealₓ'. -/
 -- see Note [lower instance priority]
 /-- The module structure from `module.complex_to_real` is a normed space. -/
 instance (priority := 900) NormedSpace.complexToReal : NormedSpace ℝ E :=
   NormedSpace.restrictScalars ℝ ℂ E
 #align normed_space.complex_to_real NormedSpace.complexToReal
 
+/- warning: complex.dist_eq -> Complex.dist_eq is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w))
+Case conversion may be inaccurate. Consider using '#align complex.dist_eq Complex.dist_eqₓ'. -/
 theorem dist_eq (z w : ℂ) : dist z w = abs (z - w) :=
   rfl
 #align complex.dist_eq Complex.dist_eq
 
+/- warning: complex.dist_eq_re_im -> Complex.dist_eq_re_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w) (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (Complex.re z) (Complex.re w)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (Complex.im z) (Complex.im w)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w) (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Complex.re z) (Complex.re w)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Complex.im z) (Complex.im w)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+Case conversion may be inaccurate. Consider using '#align complex.dist_eq_re_im Complex.dist_eq_re_imₓ'. -/
 theorem dist_eq_re_im (z w : ℂ) : dist z w = Real.sqrt ((z.re - w.re) ^ 2 + (z.im - w.im) ^ 2) :=
   by
   rw [sq, sq]
   rfl
 #align complex.dist_eq_re_im Complex.dist_eq_re_im
 
+/- warning: complex.dist_mk -> Complex.dist_mk is a dubious translation:
+lean 3 declaration is
+  forall (x₁ : Real) (y₁ : Real) (x₂ : Real) (y₂ : Real), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.mk x₁ y₁) (Complex.mk x₂ y₂)) (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x₁ x₂) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) y₁ y₂) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall (x₁ : Real) (y₁ : Real) (x₂ : Real) (y₂ : Real), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.mk x₁ y₁) (Complex.mk x₂ y₂)) (Real.sqrt (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x₁ x₂) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) y₁ y₂) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+Case conversion may be inaccurate. Consider using '#align complex.dist_mk Complex.dist_mkₓ'. -/
 @[simp]
 theorem dist_mk (x₁ y₁ x₂ y₂ : ℝ) :
     dist (mk x₁ y₁) (mk x₂ y₂) = Real.sqrt ((x₁ - x₂) ^ 2 + (y₁ - y₂) ^ 2) :=
   dist_eq_re_im _ _
 #align complex.dist_mk Complex.dist_mk
 
+/- warning: complex.dist_of_re_eq -> Complex.dist_of_re_eq is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.re z) (Complex.re w)) -> (Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w) (Dist.dist.{0} Real (PseudoMetricSpace.toHasDist.{0} Real Real.pseudoMetricSpace) (Complex.im z) (Complex.im w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.re z) (Complex.re w)) -> (Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w) (Dist.dist.{0} Real (PseudoMetricSpace.toDist.{0} Real Real.pseudoMetricSpace) (Complex.im z) (Complex.im w)))
+Case conversion may be inaccurate. Consider using '#align complex.dist_of_re_eq Complex.dist_of_re_eqₓ'. -/
 theorem dist_of_re_eq {z w : ℂ} (h : z.re = w.re) : dist z w = dist z.im w.im := by
   rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, zero_add, Real.sqrt_sq_eq_abs, Real.dist_eq]
 #align complex.dist_of_re_eq Complex.dist_of_re_eq
 
+/- warning: complex.nndist_of_re_eq -> Complex.nndist_of_re_eq is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.re z) (Complex.re w)) -> (Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w) (NNDist.nndist.{0} Real (PseudoMetricSpace.toNNDist.{0} Real Real.pseudoMetricSpace) (Complex.im z) (Complex.im w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.re z) (Complex.re w)) -> (Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w) (NNDist.nndist.{0} Real (PseudoMetricSpace.toNNDist.{0} Real Real.pseudoMetricSpace) (Complex.im z) (Complex.im w)))
+Case conversion may be inaccurate. Consider using '#align complex.nndist_of_re_eq Complex.nndist_of_re_eqₓ'. -/
 theorem nndist_of_re_eq {z w : ℂ} (h : z.re = w.re) : nndist z w = nndist z.im w.im :=
   NNReal.eq <| dist_of_re_eq h
 #align complex.nndist_of_re_eq Complex.nndist_of_re_eq
 
+/- warning: complex.edist_of_re_eq -> Complex.edist_of_re_eq is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.re z) (Complex.re w)) -> (Eq.{1} ENNReal (EDist.edist.{0} Complex (PseudoMetricSpace.toEDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w) (EDist.edist.{0} Real (PseudoMetricSpace.toEDist.{0} Real Real.pseudoMetricSpace) (Complex.im z) (Complex.im w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.re z) (Complex.re w)) -> (Eq.{1} ENNReal (EDist.edist.{0} Complex (PseudoEMetricSpace.toEDist.{0} Complex (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex)))) z w) (EDist.edist.{0} Real (PseudoEMetricSpace.toEDist.{0} Real (EMetricSpace.toPseudoEMetricSpace.{0} Real (MetricSpace.toEMetricSpace.{0} Real Real.metricSpace))) (Complex.im z) (Complex.im w)))
+Case conversion may be inaccurate. Consider using '#align complex.edist_of_re_eq Complex.edist_of_re_eqₓ'. -/
 theorem edist_of_re_eq {z w : ℂ} (h : z.re = w.re) : edist z w = edist z.im w.im := by
   rw [edist_nndist, edist_nndist, nndist_of_re_eq h]
 #align complex.edist_of_re_eq Complex.edist_of_re_eq
 
+/- warning: complex.dist_of_im_eq -> Complex.dist_of_im_eq is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.im z) (Complex.im w)) -> (Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w) (Dist.dist.{0} Real (PseudoMetricSpace.toHasDist.{0} Real Real.pseudoMetricSpace) (Complex.re z) (Complex.re w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.im z) (Complex.im w)) -> (Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w) (Dist.dist.{0} Real (PseudoMetricSpace.toDist.{0} Real Real.pseudoMetricSpace) (Complex.re z) (Complex.re w)))
+Case conversion may be inaccurate. Consider using '#align complex.dist_of_im_eq Complex.dist_of_im_eqₓ'. -/
 theorem dist_of_im_eq {z w : ℂ} (h : z.im = w.im) : dist z w = dist z.re w.re := by
   rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, add_zero, Real.sqrt_sq_eq_abs, Real.dist_eq]
 #align complex.dist_of_im_eq Complex.dist_of_im_eq
 
+/- warning: complex.nndist_of_im_eq -> Complex.nndist_of_im_eq is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.im z) (Complex.im w)) -> (Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w) (NNDist.nndist.{0} Real (PseudoMetricSpace.toNNDist.{0} Real Real.pseudoMetricSpace) (Complex.re z) (Complex.re w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.im z) (Complex.im w)) -> (Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w) (NNDist.nndist.{0} Real (PseudoMetricSpace.toNNDist.{0} Real Real.pseudoMetricSpace) (Complex.re z) (Complex.re w)))
+Case conversion may be inaccurate. Consider using '#align complex.nndist_of_im_eq Complex.nndist_of_im_eqₓ'. -/
 theorem nndist_of_im_eq {z w : ℂ} (h : z.im = w.im) : nndist z w = nndist z.re w.re :=
   NNReal.eq <| dist_of_im_eq h
 #align complex.nndist_of_im_eq Complex.nndist_of_im_eq
 
+/- warning: complex.edist_of_im_eq -> Complex.edist_of_im_eq is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.im z) (Complex.im w)) -> (Eq.{1} ENNReal (EDist.edist.{0} Complex (PseudoMetricSpace.toEDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w) (EDist.edist.{0} Real (PseudoMetricSpace.toEDist.{0} Real Real.pseudoMetricSpace) (Complex.re z) (Complex.re w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, (Eq.{1} Real (Complex.im z) (Complex.im w)) -> (Eq.{1} ENNReal (EDist.edist.{0} Complex (PseudoEMetricSpace.toEDist.{0} Complex (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex)))) z w) (EDist.edist.{0} Real (PseudoEMetricSpace.toEDist.{0} Real (EMetricSpace.toPseudoEMetricSpace.{0} Real (MetricSpace.toEMetricSpace.{0} Real Real.metricSpace))) (Complex.re z) (Complex.re w)))
+Case conversion may be inaccurate. Consider using '#align complex.edist_of_im_eq Complex.edist_of_im_eqₓ'. -/
 theorem edist_of_im_eq {z w : ℂ} (h : z.im = w.im) : edist z w = edist z.re w.re := by
   rw [edist_nndist, edist_nndist, nndist_of_im_eq h]
 #align complex.edist_of_im_eq Complex.edist_of_im_eq
 
+/- warning: complex.dist_conj_self -> Complex.dist_conj_self is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.dist_conj_self Complex.dist_conj_selfₓ'. -/
 theorem dist_conj_self (z : ℂ) : dist (conj z) z = 2 * |z.im| := by
   rw [dist_of_re_eq (conj_re z), conj_im, dist_comm, Real.dist_eq, sub_neg_eq_add, ← two_mul,
     _root_.abs_mul, abs_of_pos (zero_lt_two' ℝ)]
 #align complex.dist_conj_self Complex.dist_conj_self
 
+/- warning: complex.nndist_conj_self -> Complex.nndist_conj_self is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs (Complex.im z)))
+but is expected to have type
+  forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (HMul.hMul.{0, 0, 0} NNReal ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) (Complex.im z)) NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_self Complex.nndist_conj_selfₓ'. -/
 theorem nndist_conj_self (z : ℂ) : nndist (conj z) z = 2 * Real.nnabs z.im :=
   NNReal.eq <| by rw [← dist_nndist, NNReal.coe_mul, NNReal.coe_two, Real.coe_nnabs, dist_conj_self]
 #align complex.nndist_conj_self Complex.nndist_conj_self
 
+/- warning: complex.dist_self_conj -> Complex.dist_self_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.dist_self_conj Complex.dist_self_conjₓ'. -/
 theorem dist_self_conj (z : ℂ) : dist z (conj z) = 2 * |z.im| := by rw [dist_comm, dist_conj_self]
 #align complex.dist_self_conj Complex.dist_self_conj
 
+/- warning: complex.nndist_self_conj -> Complex.nndist_self_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs (Complex.im z)))
+but is expected to have type
+  forall (z : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} NNReal ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) (Complex.im z)) NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.nndist_self_conj Complex.nndist_self_conjₓ'. -/
 theorem nndist_self_conj (z : ℂ) : nndist z (conj z) = 2 * Real.nnabs z.im := by
   rw [nndist_comm, nndist_conj_self]
 #align complex.nndist_self_conj Complex.nndist_self_conj
 
+/- warning: complex.comap_abs_nhds_zero -> Complex.comap_abs_nhds_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Filter.{0} Complex) (Filter.comap.{0, 0} Complex Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
+but is expected to have type
+  Eq.{1} (Filter.{0} Complex) (Filter.comap.{0, 0} Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+Case conversion may be inaccurate. Consider using '#align complex.comap_abs_nhds_zero Complex.comap_abs_nhds_zeroₓ'. -/
 @[simp]
 theorem comap_abs_nhds_zero : Filter.comap abs (𝓝 0) = 𝓝 0 :=
   comap_norm_nhds_zero
 #align complex.comap_abs_nhds_zero Complex.comap_abs_nhds_zero
 
+/- warning: complex.norm_real -> Complex.norm_real is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (Norm.norm.{0} Real Real.hasNorm r)
+but is expected to have type
+  forall (r : Real), Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Complex.ofReal' r)) (Norm.norm.{0} Real Real.norm r)
+Case conversion may be inaccurate. Consider using '#align complex.norm_real Complex.norm_realₓ'. -/
 theorem norm_real (r : ℝ) : ‖(r : ℂ)‖ = ‖r‖ :=
   abs_ofReal _
 #align complex.norm_real Complex.norm_real
 
+/- warning: complex.norm_rat -> Complex.norm_rat is a dubious translation:
+lean 3 declaration is
+  forall (r : Rat), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (NormedDivisionRing.toDivisionRing.{0} Complex (NormedField.toNormedDivisionRing.{0} Complex Complex.normedField)))))) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) r))
+but is expected to have type
+  forall (r : Rat), Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Rat.cast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Rat.cast.{0} Real Real.ratCast r))
+Case conversion may be inaccurate. Consider using '#align complex.norm_rat Complex.norm_ratₓ'. -/
 @[simp]
 theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| :=
   by
@@ -167,70 +281,152 @@ theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| :=
   exact norm_real _
 #align complex.norm_rat Complex.norm_rat
 
+/- warning: complex.norm_nat -> Complex.norm_nat is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) (Nat.cast.{0} Real Real.natCast n)
+Case conversion may be inaccurate. Consider using '#align complex.norm_nat Complex.norm_natₓ'. -/
 @[simp]
 theorem norm_nat (n : ℕ) : ‖(n : ℂ)‖ = n :=
   abs_of_nat _
 #align complex.norm_nat Complex.norm_nat
 
+/- warning: complex.norm_int -> Complex.norm_int is a dubious translation:
+lean 3 declaration is
+  forall {n : Int}, Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n))
+but is expected to have type
+  forall {n : Int}, Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Int.cast.{0} Real Real.intCast n))
+Case conversion may be inaccurate. Consider using '#align complex.norm_int Complex.norm_intₓ'. -/
 @[simp]
 theorem norm_int {n : ℤ} : ‖(n : ℂ)‖ = |n| := by
   simp (config := { singlePass := true }) [← Rat.cast_coe_int]
 #align complex.norm_int Complex.norm_int
 
+/- warning: complex.norm_int_of_nonneg -> Complex.norm_int_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {n : Int}, (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) n) -> (Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n))
+but is expected to have type
+  forall {n : Int}, (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) n) -> (Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Int.cast.{0} Real Real.intCast n))
+Case conversion may be inaccurate. Consider using '#align complex.norm_int_of_nonneg Complex.norm_int_of_nonnegₓ'. -/
 theorem norm_int_of_nonneg {n : ℤ} (hn : 0 ≤ n) : ‖(n : ℂ)‖ = n := by simp [hn]
 #align complex.norm_int_of_nonneg Complex.norm_int_of_nonneg
 
+/- warning: complex.continuous_abs -> Complex.continuous_abs is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)
+but is expected to have type
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)
+Case conversion may be inaccurate. Consider using '#align complex.continuous_abs Complex.continuous_absₓ'. -/
 @[continuity]
 theorem continuous_abs : Continuous abs :=
   continuous_norm
 #align complex.continuous_abs Complex.continuous_abs
 
+/- warning: complex.continuous_norm_sq -> Complex.continuous_normSq is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq)
+but is expected to have type
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq)
+Case conversion may be inaccurate. Consider using '#align complex.continuous_norm_sq Complex.continuous_normSqₓ'. -/
 @[continuity]
 theorem continuous_normSq : Continuous normSq := by
   simpa [← norm_sq_eq_abs] using continuous_abs.pow 2
 #align complex.continuous_norm_sq Complex.continuous_normSq
 
+/- warning: complex.nnnorm_real -> Complex.nnnorm_real is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} NNReal (NNNorm.nnnorm.{0} Complex (SeminormedAddGroup.toNNNorm.{0} Complex (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (NNNorm.nnnorm.{0} Real (SeminormedAddGroup.toNNNorm.{0} Real (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) r)
+but is expected to have type
+  forall (r : Real), Eq.{1} NNReal (NNNorm.nnnorm.{0} Complex (SeminormedAddGroup.toNNNorm.{0} Complex (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.ofReal' r)) (NNNorm.nnnorm.{0} Real (SeminormedAddGroup.toNNNorm.{0} Real (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) r)
+Case conversion may be inaccurate. Consider using '#align complex.nnnorm_real Complex.nnnorm_realₓ'. -/
 @[simp, norm_cast]
 theorem nnnorm_real (r : ℝ) : ‖(r : ℂ)‖₊ = ‖r‖₊ :=
   Subtype.ext <| norm_real r
 #align complex.nnnorm_real Complex.nnnorm_real
 
+/- warning: complex.nnnorm_nat -> Complex.nnnorm_nat is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{0} Complex (SeminormedAddGroup.toNNNorm.{0} Complex (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{0} Complex (SeminormedAddGroup.toNNNorm.{0} Complex (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n)
+Case conversion may be inaccurate. Consider using '#align complex.nnnorm_nat Complex.nnnorm_natₓ'. -/
 @[simp, norm_cast]
 theorem nnnorm_nat (n : ℕ) : ‖(n : ℂ)‖₊ = n :=
   Subtype.ext <| by simp
 #align complex.nnnorm_nat Complex.nnnorm_nat
 
+/- warning: complex.nnnorm_int -> Complex.nnnorm_int is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} NNReal (NNNorm.nnnorm.{0} Complex (SeminormedAddGroup.toNNNorm.{0} Complex (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n)) (NNNorm.nnnorm.{0} Int (SeminormedAddGroup.toNNNorm.{0} Int (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Int (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Int (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Int (NormedRing.toNonUnitalNormedRing.{0} Int (NormedCommRing.toNormedRing.{0} Int Int.normedCommRing)))))) n)
+but is expected to have type
+  forall (n : Int), Eq.{1} NNReal (NNNorm.nnnorm.{0} Complex (SeminormedAddGroup.toNNNorm.{0} Complex (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (NNNorm.nnnorm.{0} Int (SeminormedAddGroup.toNNNorm.{0} Int (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Int (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Int (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Int (NormedRing.toNonUnitalNormedRing.{0} Int (NormedCommRing.toNormedRing.{0} Int Int.normedCommRing)))))) n)
+Case conversion may be inaccurate. Consider using '#align complex.nnnorm_int Complex.nnnorm_intₓ'. -/
 @[simp, norm_cast]
 theorem nnnorm_int (n : ℤ) : ‖(n : ℂ)‖₊ = ‖n‖₊ :=
   Subtype.ext <| by simp only [coe_nnnorm, norm_int, Int.norm_eq_abs]
 #align complex.nnnorm_int Complex.nnnorm_int
 
+/- warning: complex.nnnorm_eq_one_of_pow_eq_one -> Complex.nnnorm_eq_one_of_pow_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {ζ : Complex} {n : Nat}, (Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) ζ n) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) -> (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{1} NNReal (NNNorm.nnnorm.{0} Complex (SeminormedAddGroup.toNNNorm.{0} Complex (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) ζ) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
+but is expected to have type
+  forall {ζ : Complex} {n : Nat}, (Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) ζ n) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) -> (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{1} NNReal (NNNorm.nnnorm.{0} Complex (SeminormedAddGroup.toNNNorm.{0} Complex (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) ζ) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)))
+Case conversion may be inaccurate. Consider using '#align complex.nnnorm_eq_one_of_pow_eq_one Complex.nnnorm_eq_one_of_pow_eq_oneₓ'. -/
 theorem nnnorm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖₊ = 1 :=
   by
   refine' (@pow_left_inj NNReal _ _ _ _ zero_le' zero_le' hn.bot_lt).mp _
   rw [← nnnorm_pow, h, nnnorm_one, one_pow]
 #align complex.nnnorm_eq_one_of_pow_eq_one Complex.nnnorm_eq_one_of_pow_eq_one
 
+/- warning: complex.norm_eq_one_of_pow_eq_one -> Complex.norm_eq_one_of_pow_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {ζ : Complex} {n : Nat}, (Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) ζ n) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) -> (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{1} Real (Norm.norm.{0} Complex Complex.hasNorm ζ) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {ζ : Complex} {n : Nat}, (Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) ζ n) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) -> (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{1} Real (Norm.norm.{0} Complex Complex.instNormComplex ζ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align complex.norm_eq_one_of_pow_eq_one Complex.norm_eq_one_of_pow_eq_oneₓ'. -/
 theorem norm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖ = 1 :=
   congr_arg coe (nnnorm_eq_one_of_pow_eq_one h hn)
 #align complex.norm_eq_one_of_pow_eq_one Complex.norm_eq_one_of_pow_eq_one
 
+/- warning: complex.equiv_real_prod_apply_le -> Complex.equivRealProd_apply_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) z) (Prod.toNorm.{0, 0} Real Real Real.norm Real.norm) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
+Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_apply_le Complex.equivRealProd_apply_leₓ'. -/
 theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ abs z := by
   simp [Prod.norm_def, abs_re_le_abs, abs_im_le_abs]
 #align complex.equiv_real_prod_apply_le Complex.equivRealProd_apply_le
 
+/- warning: complex.equiv_real_prod_apply_le' -> Complex.equivRealProd_apply_le' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) z) (Prod.toNorm.{0, 0} Real Real Real.norm Real.norm) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd z)) (HMul.hMul.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z))
+Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_apply_le' Complex.equivRealProd_apply_le'ₓ'. -/
 theorem equivRealProd_apply_le' (z : ℂ) : ‖equivRealProd z‖ ≤ 1 * abs z := by
   simpa using equiv_real_prod_apply_le z
 #align complex.equiv_real_prod_apply_le' Complex.equivRealProd_apply_le'
 
+#print Complex.lipschitz_equivRealProd /-
 theorem lipschitz_equivRealProd : LipschitzWith 1 equivRealProd := by
   simpa using AddMonoidHomClass.lipschitz_of_bound equiv_real_prod_lm 1 equiv_real_prod_apply_le'
 #align complex.lipschitz_equiv_real_prod Complex.lipschitz_equivRealProd
+-/
 
+#print Complex.antilipschitz_equivRealProd /-
 theorem antilipschitz_equivRealProd : AntilipschitzWith (NNReal.sqrt 2) equivRealProd := by
   simpa using AddMonoidHomClass.antilipschitz_of_bound equiv_real_prod_lm abs_le_sqrt_two_mul_max
 #align complex.antilipschitz_equiv_real_prod Complex.antilipschitz_equivRealProd
+-/
 
+/- warning: complex.uniform_embedding_equiv_real_prod -> Complex.uniformEmbedding_equivRealProd is a dubious translation:
+lean 3 declaration is
+  UniformEmbedding.{0, 0} Complex (Prod.{0, 0} Real Real) (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Prod.uniformSpace.{0, 0} Real Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) (fun (_x : Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) => Complex -> (Prod.{0, 0} Real Real)) (Equiv.hasCoeToFun.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd)
+but is expected to have type
+  UniformEmbedding.{0, 0} Complex (Prod.{0, 0} Real Real) (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (instUniformSpaceProd.{0, 0} Real Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Complex) => Prod.{0, 0} Real Real) _x) (Equiv.instFunLikeEquiv.{1, 1} Complex (Prod.{0, 0} Real Real)) Complex.equivRealProd)
+Case conversion may be inaccurate. Consider using '#align complex.uniform_embedding_equiv_real_prod Complex.uniformEmbedding_equivRealProdₓ'. -/
 theorem uniformEmbedding_equivRealProd : UniformEmbedding equivRealProd :=
   antilipschitz_equivRealProd.UniformEmbedding lipschitz_equivRealProd.UniformContinuous
 #align complex.uniform_embedding_equiv_real_prod Complex.uniformEmbedding_equivRealProd
@@ -238,6 +434,12 @@ theorem uniformEmbedding_equivRealProd : UniformEmbedding equivRealProd :=
 instance : CompleteSpace ℂ :=
   (completeSpace_congr uniformEmbedding_equivRealProd).mpr inferInstance
 
+/- warning: complex.equiv_real_prod_clm -> Complex.equivRealProdClm is a dubious translation:
+lean 3 declaration is
+  ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Prod.{0, 0} Real Real) (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Prod.addCommMonoid.{0, 0} Real Real Real.addCommMonoid Real.addCommMonoid) (Complex.module.{0} Real Real.semiring Real.module) (Prod.module.{0, 0, 0} Real Real Real Real.semiring Real.addCommMonoid Real.addCommMonoid Real.module Real.module)
+but is expected to have type
+  ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Prod.{0, 0} Real Real) (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Prod.instAddCommMonoidSum.{0, 0} Real Real Real.instAddCommMonoidReal Real.instAddCommMonoidReal) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Prod.module.{0, 0, 0} Real Real Real Real.semiring Real.instAddCommMonoidReal Real.instAddCommMonoidReal (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))
+Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_clm Complex.equivRealProdClmₓ'. -/
 /-- The natural `continuous_linear_equiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
 def equivRealProdClm : ℂ ≃L[ℝ] ℝ × ℝ :=
@@ -248,60 +450,118 @@ def equivRealProdClm : ℂ ≃L[ℝ] ℝ × ℝ :=
 instance : ProperSpace ℂ :=
   (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdClm.toHomeomorph).ProperSpace
 
+#print Complex.tendsto_abs_cocompact_atTop /-
 /-- The `abs` function on `ℂ` is proper. -/
 theorem tendsto_abs_cocompact_atTop : Filter.Tendsto abs (Filter.cocompact ℂ) Filter.atTop :=
   tendsto_norm_cocompact_atTop
 #align complex.tendsto_abs_cocompact_at_top Complex.tendsto_abs_cocompact_atTop
+-/
 
+#print Complex.tendsto_normSq_cocompact_atTop /-
 /-- The `norm_sq` function on `ℂ` is proper. -/
 theorem tendsto_normSq_cocompact_atTop : Filter.Tendsto normSq (Filter.cocompact ℂ) Filter.atTop :=
   by
   simpa [mul_self_abs] using
     tendsto_abs_cocompact_at_top.at_top_mul_at_top tendsto_abs_cocompact_at_top
 #align complex.tendsto_norm_sq_cocompact_at_top Complex.tendsto_normSq_cocompact_atTop
+-/
 
 open ContinuousLinearMap
 
+/- warning: complex.re_clm -> Complex.reClm is a dubious translation:
+lean 3 declaration is
+  ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module
+but is expected to have type
+  ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))
+Case conversion may be inaccurate. Consider using '#align complex.re_clm Complex.reClmₓ'. -/
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
 def reClm : ℂ →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by simp [abs_re_le_abs]
 #align complex.re_clm Complex.reClm
 
+/- warning: complex.continuous_re -> Complex.continuous_re is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
+but is expected to have type
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
+Case conversion may be inaccurate. Consider using '#align complex.continuous_re Complex.continuous_reₓ'. -/
 @[continuity]
 theorem continuous_re : Continuous re :=
   reClm.Continuous
 #align complex.continuous_re Complex.continuous_re
 
+/- warning: complex.re_clm_coe -> Complex.reClm_coe is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (HasLiftT.mk.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (CoeTCₓ.coe.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (coeBase.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (ContinuousLinearMap.LinearMap.coe.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module)))) Complex.reClm) Complex.reLm
+but is expected to have type
+  Eq.{1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (ContinuousLinearMap.toLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) Complex.reClm) Complex.reLm
+Case conversion may be inaccurate. Consider using '#align complex.re_clm_coe Complex.reClm_coeₓ'. -/
 @[simp]
 theorem reClm_coe : (coe reClm : ℂ →ₗ[ℝ] ℝ) = reLm :=
   rfl
 #align complex.re_clm_coe Complex.reClm_coe
 
+/- warning: complex.re_clm_apply -> Complex.reClm_apply is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (fun (_x : ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) => Complex -> Real) (ContinuousLinearMap.toFun.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) Complex.reClm z) (Complex.re z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Real) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) Complex.reClm z) (Complex.re z)
+Case conversion may be inaccurate. Consider using '#align complex.re_clm_apply Complex.reClm_applyₓ'. -/
 @[simp]
 theorem reClm_apply (z : ℂ) : (reClm : ℂ → ℝ) z = z.re :=
   rfl
 #align complex.re_clm_apply Complex.reClm_apply
 
+/- warning: complex.im_clm -> Complex.imClm is a dubious translation:
+lean 3 declaration is
+  ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module
+but is expected to have type
+  ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))
+Case conversion may be inaccurate. Consider using '#align complex.im_clm Complex.imClmₓ'. -/
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
 def imClm : ℂ →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by simp [abs_im_le_abs]
 #align complex.im_clm Complex.imClm
 
+/- warning: complex.continuous_im -> Complex.continuous_im is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
+but is expected to have type
+  Continuous.{0, 0} Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
+Case conversion may be inaccurate. Consider using '#align complex.continuous_im Complex.continuous_imₓ'. -/
 @[continuity]
 theorem continuous_im : Continuous im :=
   imClm.Continuous
 #align complex.continuous_im Complex.continuous_im
 
+/- warning: complex.im_clm_coe -> Complex.imClm_coe is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (HasLiftT.mk.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (CoeTCₓ.coe.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (coeBase.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (ContinuousLinearMap.LinearMap.coe.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module)))) Complex.imClm) Complex.imLm
+but is expected to have type
+  Eq.{1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (ContinuousLinearMap.toLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) Complex.imClm) Complex.imLm
+Case conversion may be inaccurate. Consider using '#align complex.im_clm_coe Complex.imClm_coeₓ'. -/
 @[simp]
 theorem imClm_coe : (coe imClm : ℂ →ₗ[ℝ] ℝ) = imLm :=
   rfl
 #align complex.im_clm_coe Complex.imClm_coe
 
+/- warning: complex.im_clm_apply -> Complex.imClm_apply is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) (fun (_x : ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) => Complex -> Real) (ContinuousLinearMap.toFun.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (Complex.module.{0} Real Real.semiring Real.module) Real.module) Complex.imClm z) (Complex.im z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Real) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex Real (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) Complex.imClm z) (Complex.im z)
+Case conversion may be inaccurate. Consider using '#align complex.im_clm_apply Complex.imClm_applyₓ'. -/
 @[simp]
 theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
   rfl
 #align complex.im_clm_apply Complex.imClm_apply
 
+/- warning: complex.restrict_scalars_one_smul_right' -> Complex.restrictScalars_one_smul_right' is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.restrictScalars.{0, 0, u1, 0} Complex Complex E Complex.ring Complex.addCommGroup (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.ring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LinearMap.IsScalarTower.compatibleSMul.{0, u1, 0, 0} Complex E (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Complex (Ring.toSemiring.{0} Complex Complex.ring) (Complex.hasSmul.{0} Real (Mul.toSMul.{0} Real Real.hasMul)) (SMulZeroClass.toHasSmul.{0, 0} Real Complex (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (SMulWithZero.toSmulZeroClass.{0, 0} Real Complex (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring))))) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring)) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (Module.toMulActionWithZero.{0, 0} Real Complex (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (Module.real_complex_tower.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} 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(SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) Real.module (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E Real.monoid (MulActionWithZero.toMulAction.{0, u1} Real E Real.monoidWithZero (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.reClm x) (SMul.smul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (SMulZeroClass.toHasSmul.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddMonoid.toAddZeroClass.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Complex (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (Ring.toSemiring.{0} Complex Complex.ring) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (ContinuousLinearMap.module.{0, 0, 0, 0, u1} Real Real Complex (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Complex Complex.ring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulCommClass.complexToReal.{0, u1} Complex E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Complex (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) (LipschitzAdd.continuousAdd.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.module.{0} Real Real.semiring Real.module) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) Real.module (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E Real.monoid (MulActionWithZero.toMulAction.{0, u1} Real E Real.monoidWithZero (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (SeminormedAddGroup.toAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] (x : E), Eq.{succ u1} (ContinuousLinearMap.{0, 0, 0, u1} Real Real (Ring.toSemiring.{0} Real Real.instRingReal) (Ring.toSemiring.{0} Real Real.instRingReal) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.restrictScalars.{0, 0, u1, 0} Complex Complex E Complex.instRingComplex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) Real Real.instRingReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (LinearMap.IsScalarTower.compatibleSMul.{0, u1, 0, 0} Complex E (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) Real Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) (Complex.instSMulComplex.{0} Real (Algebra.toSMul.{0, 0} Real Real Real.instCommSemiringReal Real.semiring (NormedAlgebra.toAlgebra.{0, 0} Real Real Real.normedField (SeminormedCommRing.toSeminormedRing.{0} Real (NormedCommRing.toSeminormedCommRing.{0} Real Real.normedCommRing)) (IsROrC.toNormedAlgebra.{0} Real Real.isROrC)))) (SMulZeroClass.toSMul.{0, 0} Real Complex (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (SMulWithZero.toSMulZeroClass.{0, 0} Real Complex (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal)) (NegZeroClass.toZero.{0} Complex (SubNegZeroMonoid.toNegZeroClass.{0} Complex (SubtractionMonoid.toSubNegZeroMonoid.{0} Complex (SubtractionCommMonoid.toSubtractionMonoid.{0} Complex (AddCommGroup.toDivisionAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))))) (Module.toMulActionWithZero.{0, 0} Real Complex (Ring.toSemiring.{0} Real Real.instRingReal) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} 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(SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (Module.real_complex_tower.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (NormedSpace.toModule.{0, 0} Complex Complex Complex.instNormedFieldComplex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedField.toNormedSpace.{0} Complex Complex.instNormedFieldComplex)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2) (IsScalarTower.left.{0, u1} Complex E (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (MulActionWithZero.toMulAction.{0, u1} Complex E 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(SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)) (OfNat.ofNat.{0} (ContinuousLinearMap.{0, 0, 0, 0} Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (RingHom.id.{0} Complex 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(NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.add.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E 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(AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) (ContinuousLinearMap.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (smulCommClass_self.{0, u1} Complex E (CommRing.toCommMonoid.{0} Complex Complex.commRing) (MulActionWithZero.toMulAction.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (ContinuousSMul.continuousConstSMul.{0, u1} Complex E (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex 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Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (BoundedSMul.continuousSMul.{0, u1} Complex E (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Complex E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E (MonoidWithZero.toZero.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (NormedSpace.boundedSMul.{0, u1} Complex E Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))))))))) Complex.I (ContinuousLinearMap.smulRight.{0, u1, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) Real Real Real.semiring Real.semiring (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)) (IsScalarTower.left.{0, u1} Real E (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (MulActionWithZero.toMulAction.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2)))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) (NormedSpace.complexToReal.{u1} E _inst_1 _inst_2))) Complex.imClm x)))
+Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smul_right'ₓ'. -/
 theorem restrictScalars_one_smul_right' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =
       reClm.smul_right x + I • imClm.smul_right x :=
@@ -310,6 +570,12 @@ theorem restrictScalars_one_smul_right' (x : E) :
   simp [mk_eq_add_mul_I, add_smul, mul_smul, smul_comm I]
 #align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smul_right'
 
+/- warning: complex.restrict_scalars_one_smul_right -> Complex.restrictScalars_one_smulRight is a dubious translation:
+lean 3 declaration is
+  forall (x : Complex), Eq.{1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module)) (ContinuousLinearMap.restrictScalars.{0, 0, 0, 0} Complex Complex Complex Complex.ring Complex.addCommGroup Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Real Real.ring (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (LinearMap.IsScalarTower.compatibleSMul.{0, 0, 0, 0} Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real Complex (Ring.toSemiring.{0} Complex Complex.ring) (Complex.hasSmul.{0} Real (Mul.toSMul.{0} Real Real.hasMul)) (SMulZeroClass.toHasSmul.{0, 0} Real Complex (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (SMulWithZero.toSmulZeroClass.{0, 0} Real Complex (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring))))) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring)) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (Module.toMulActionWithZero.{0, 0} Real Complex (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField))) (SMulZeroClass.toHasSmul.{0, 0} Real Complex (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (SMulWithZero.toSmulZeroClass.{0, 0} Real Complex (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring))))) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real Real.ring)) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (Module.toMulActionWithZero.{0, 0} Real Complex (Ring.toSemiring.{0} Real Real.ring) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module))))) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (Module.real_complex_tower.{0} Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)))) (ContinuousLinearMap.smulRight.{0, 0, 0, 0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex Complex (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (IsScalarTower.right.{0, 0} Complex Complex Complex.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Algebra.id.{0} Complex Complex.commSemiring)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (ContinuousMul.to_continuousSMul.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) Complex.hasMul (semi_normed_ring_top_monoid.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (OfNat.ofNat.{0} (ContinuousLinearMap.{0, 0, 0, 0} Complex Complex (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex 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Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module)) (AddCommMonoid.toAddMonoid.{0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module)) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (LipschitzAdd.continuousAdd.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne)) (SeminormedAddCommGroup.to_lipschitzAdd.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))))))) (Module.toMulActionWithZero.{0, 0} Complex (ContinuousLinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module)) (Ring.toSemiring.{0} Complex Complex.ring) (ContinuousLinearMap.addCommMonoid.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (LipschitzAdd.continuousAdd.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne)) (SeminormedAddCommGroup.to_lipschitzAdd.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (ContinuousLinearMap.module.{0, 0, 0, 0, 0} Real Real Complex (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Complex Complex.ring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (SMulCommClass.complexToReal.{0, 0} Complex Complex Complex.addCommGroup (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)) (SMulZeroClass.toHasSmul.{0, 0} Complex Complex (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (SMulWithZero.toSmulZeroClass.{0, 0} Complex Complex (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (MulActionWithZero.toSMulWithZero.{0, 0} Complex Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (Module.toMulActionWithZero.{0, 0} Complex Complex (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)))))) (smulCommClass_self.{0, 0} Complex Complex (CommRing.toCommMonoid.{0} Complex Complex.commRing) (Monoid.toMulAction.{0} Complex (CommMonoid.toMonoid.{0} Complex (CommRing.toCommMonoid.{0} Complex Complex.commRing))))) (SMulCommClass.continuousConstSMul.{0, 0} Complex Complex (Ring.toMonoid.{0} Complex Complex.ring) (SMulZeroClass.toHasSmul.{0, 0} Complex Complex (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (SMulWithZero.toSmulZeroClass.{0, 0} Complex Complex (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (MulActionWithZero.toSMulWithZero.{0, 0} Complex Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup)))) (Module.toMulActionWithZero.{0, 0} Complex Complex (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (NormedSpace.toModule.{0, 0} Complex Complex Complex.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NormedField.toNormedSpace.{0} Complex Complex.normedField)))))) (Algebra.to_smulCommClass.{0, 0} Complex Complex Complex.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Algebra.id.{0} Complex Complex.commSemiring)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (semi_normed_ring_top_monoid.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) (LipschitzAdd.continuousAdd.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne)) (SeminormedAddCommGroup.to_lipschitzAdd.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))))))) x (OfNat.ofNat.{0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module)) 1 (OfNat.mk.{0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module)) 1 (One.one.{0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.ring) (Ring.toSemiring.{0} Real Real.ring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.ring))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module)) (ContinuousLinearMap.one.{0, 0} Real (Ring.toSemiring.{0} Real Real.ring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real (Ring.toSemiring.{0} Real Real.ring) Real.module))))))
+but is expected to have type
+  forall (x : Complex), Eq.{1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real Real.instRingReal) (Ring.toSemiring.{0} Real Real.instRingReal) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real Real.instRingReal))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex 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+Case conversion may be inaccurate. Consider using '#align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRightₓ'. -/
 theorem restrictScalars_one_smulRight (x : ℂ) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] ℂ) = x • 1 :=
   by
@@ -318,39 +584,87 @@ theorem restrictScalars_one_smulRight (x : ℂ) :
   apply mul_comm
 #align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRight
 
+/- warning: complex.conj_lie -> Complex.conjLie is a dubious translation:
+lean 3 declaration is
+  LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)
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+Case conversion may be inaccurate. Consider using '#align complex.conj_lie Complex.conjLieₓ'. -/
 /-- The complex-conjugation function from `ℂ` to itself is an isometric linear equivalence. -/
 def conjLie : ℂ ≃ₗᵢ[ℝ] ℂ :=
   ⟨conjAe.toLinearEquiv, abs_conj⟩
 #align complex.conj_lie Complex.conjLie
 
+/- warning: complex.conj_lie_apply -> Complex.conjLie_apply is a dubious translation:
+lean 3 declaration is
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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometryEquiv.{0, 0, 0, 0} Real Real 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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) Complex.conjLie z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)
+Case conversion may be inaccurate. Consider using '#align complex.conj_lie_apply Complex.conjLie_applyₓ'. -/
 @[simp]
 theorem conjLie_apply (z : ℂ) : conjLie z = conj z :=
   rfl
 #align complex.conj_lie_apply Complex.conjLie_apply
 
+/- warning: complex.conj_lie_symm -> Complex.conjLie_symm is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.symm.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) Complex.conjLie) Complex.conjLie
+but is expected to have type
+  Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.symm.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex.conjLie) Complex.conjLie
+Case conversion may be inaccurate. Consider using '#align complex.conj_lie_symm Complex.conjLie_symmₓ'. -/
 @[simp]
 theorem conjLie_symm : conjLie.symm = conjLie :=
   rfl
 #align complex.conj_lie_symm Complex.conjLie_symm
 
+/- warning: complex.isometry_conj -> Complex.isometry_conj is a dubious translation:
+lean 3 declaration is
+  Isometry.{0, 0} Complex Complex (PseudoMetricSpace.toPseudoEMetricSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (PseudoMetricSpace.toPseudoEMetricSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing))
+but is expected to have type
+  Isometry.{0, 0} Complex Complex (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex))) (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
+Case conversion may be inaccurate. Consider using '#align complex.isometry_conj Complex.isometry_conjₓ'. -/
 theorem isometry_conj : Isometry (conj : ℂ → ℂ) :=
   conjLie.Isometry
 #align complex.isometry_conj Complex.isometry_conj
 
+/- warning: complex.dist_conj_conj -> Complex.dist_conj_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)) (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w)
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)) (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w)
+Case conversion may be inaccurate. Consider using '#align complex.dist_conj_conj Complex.dist_conj_conjₓ'. -/
 @[simp]
 theorem dist_conj_conj (z w : ℂ) : dist (conj z) (conj w) = dist z w :=
   isometry_conj.dist_eq z w
 #align complex.dist_conj_conj Complex.dist_conj_conj
 
+/- warning: complex.nndist_conj_conj -> Complex.nndist_conj_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z w)
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z w)
+Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_conj Complex.nndist_conj_conjₓ'. -/
 @[simp]
 theorem nndist_conj_conj (z w : ℂ) : nndist (conj z) (conj w) = nndist z w :=
   isometry_conj.nndist_eq z w
 #align complex.nndist_conj_conj Complex.nndist_conj_conj
 
+/- warning: complex.dist_conj_comm -> Complex.dist_conj_comm is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) w) (Dist.dist.{0} Complex (PseudoMetricSpace.toHasDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Dist.dist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) w) (Dist.dist.{0} Complex (PseudoMetricSpace.toDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w))
+Case conversion may be inaccurate. Consider using '#align complex.dist_conj_comm Complex.dist_conj_commₓ'. -/
 theorem dist_conj_comm (z w : ℂ) : dist (conj z) w = dist z (conj w) := by
   rw [← dist_conj_conj, conj_conj]
 #align complex.dist_conj_comm Complex.dist_conj_comm
 
+/- warning: complex.nndist_conj_comm -> Complex.nndist_conj_comm is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) w) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} NNReal (NNDist.nndist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (PseudoMetricSpace.toNNDist.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedRing.toPseudoMetricSpace.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (SeminormedCommRing.toSeminormedRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedCommRing.toSeminormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (NormedField.toNormedCommRing.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instNormedFieldComplex))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) w) (NNDist.nndist.{0} Complex (PseudoMetricSpace.toNNDist.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex 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(NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w))
+Case conversion may be inaccurate. Consider using '#align complex.nndist_conj_comm Complex.nndist_conj_commₓ'. -/
 theorem nndist_conj_comm (z w : ℂ) : nndist (conj z) w = nndist z (conj w) :=
   Subtype.ext <| dist_conj_comm _ _
 #align complex.nndist_conj_comm Complex.nndist_conj_comm
@@ -358,11 +672,23 @@ theorem nndist_conj_comm (z w : ℂ) : nndist (conj z) w = nndist z (conj w) :=
 instance : ContinuousStar ℂ :=
   ⟨conjLie.Continuous⟩
 
+/- warning: complex.continuous_conj -> Complex.continuous_conj is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing))
+but is expected to have type
+  Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
+Case conversion may be inaccurate. Consider using '#align complex.continuous_conj Complex.continuous_conjₓ'. -/
 @[continuity]
 theorem continuous_conj : Continuous (conj : ℂ → ℂ) :=
   continuous_star
 #align complex.continuous_conj Complex.continuous_conj
 
+/- warning: complex.ring_hom_eq_id_or_conj_of_continuous -> Complex.ringHom_eq_id_or_conj_of_continuous is a dubious translation:
+lean 3 declaration is
+  forall {f : RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))}, (Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f)) -> (Or (Eq.{1} (RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f (RingHom.id.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) (Eq.{1} (RingHom.{0, 0} Complex Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing)))
+but is expected to have type
+  forall {f : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)}, (Continuous.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) f)) -> (Or (Eq.{1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (Eq.{1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing)))
+Case conversion may be inaccurate. Consider using '#align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuousₓ'. -/
 /-- The only continuous ring homomorphisms from `ℂ` to `ℂ` are the identity and the complex
 conjugation. -/
 theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous f) :
@@ -373,35 +699,77 @@ theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous
   all_goals convert congr_arg AlgHom.toRingHom h; ext1; rfl
 #align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuous
 
+/- warning: complex.conj_cle -> Complex.conjCle is a dubious translation:
+lean 3 declaration is
+  ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)
+but is expected to have type
+  ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))
+Case conversion may be inaccurate. Consider using '#align complex.conj_cle Complex.conjCleₓ'. -/
 /-- Continuous linear equiv version of the conj function, from `ℂ` to `ℂ`. -/
 def conjCle : ℂ ≃L[ℝ] ℂ :=
   conjLie
 #align complex.conj_cle Complex.conjCle
 
+/- warning: complex.conj_cle_coe -> Complex.conjCle_coe is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (ContinuousLinearEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) Complex.conjCle) (AlgEquiv.toLinearEquiv.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) Complex.conjAe)
+but is expected to have type
+  Eq.{1} (LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (ContinuousLinearEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex.conjCle) (AlgEquiv.toLinearEquiv.{0, 0, 0} Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) Complex.conjAe)
+Case conversion may be inaccurate. Consider using '#align complex.conj_cle_coe Complex.conjCle_coeₓ'. -/
 @[simp]
 theorem conjCle_coe : conjCle.toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
 #align complex.conj_cle_coe Complex.conjCle_coe
 
+/- warning: complex.conj_cle_apply -> Complex.conjCle_apply is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (fun (_x : ContinuousLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) => Complex -> Complex) (ContinuousLinearEquiv.hasCoeToFun.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) Complex.conjCle z) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)
+but is expected to have type
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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) Complex.conjCle z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)
+Case conversion may be inaccurate. Consider using '#align complex.conj_cle_apply Complex.conjCle_applyₓ'. -/
 @[simp]
 theorem conjCle_apply (z : ℂ) : conjCle z = conj z :=
   rfl
 #align complex.conj_cle_apply Complex.conjCle_apply
 
+/- warning: complex.of_real_li -> Complex.ofRealLi is a dubious translation:
+lean 3 declaration is
+  LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) Real.module (Complex.module.{0} Real Real.semiring Real.module)
+but is expected to have type
+  LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_li Complex.ofRealLiₓ'. -/
 /-- Linear isometry version of the canonical embedding of `ℝ` in `ℂ`. -/
 def ofRealLi : ℝ →ₗᵢ[ℝ] ℂ :=
   ⟨ofRealAm.toLinearMap, norm_real⟩
 #align complex.of_real_li Complex.ofRealLi
 
-theorem isometry_of_real : Isometry (coe : ℝ → ℂ) :=
+/- warning: complex.isometry_of_real -> Complex.isometry_ofReal is a dubious translation:
+lean 3 declaration is
+  Isometry.{0, 0} Real Complex (PseudoMetricSpace.toPseudoEMetricSpace.{0} Real Real.pseudoMetricSpace) (PseudoMetricSpace.toPseudoEMetricSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))))
+but is expected to have type
+  Isometry.{0, 0} Real Complex (EMetricSpace.toPseudoEMetricSpace.{0} Real (MetricSpace.toEMetricSpace.{0} Real Real.metricSpace)) (EMetricSpace.toPseudoEMetricSpace.{0} Complex (MetricSpace.toEMetricSpace.{0} Complex (NormedField.toMetricSpace.{0} Complex Complex.instNormedFieldComplex))) Complex.ofReal'
+Case conversion may be inaccurate. Consider using '#align complex.isometry_of_real Complex.isometry_ofRealₓ'. -/
+theorem isometry_ofReal : Isometry (coe : ℝ → ℂ) :=
   ofRealLi.Isometry
-#align complex.isometry_of_real Complex.isometry_of_real
-
+#align complex.isometry_of_real Complex.isometry_ofReal
+
+/- warning: complex.continuous_of_real -> Complex.continuous_ofReal is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))))
+but is expected to have type
+  Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) Complex.ofReal'
+Case conversion may be inaccurate. Consider using '#align complex.continuous_of_real Complex.continuous_ofRealₓ'. -/
 @[continuity]
-theorem continuous_of_real : Continuous (coe : ℝ → ℂ) :=
+theorem continuous_ofReal : Continuous (coe : ℝ → ℂ) :=
   ofRealLi.Continuous
-#align complex.continuous_of_real Complex.continuous_of_real
-
+#align complex.continuous_of_real Complex.continuous_ofReal
+
+/- warning: complex.ring_hom_eq_of_real_of_continuous -> Complex.ringHom_eq_ofReal_of_continuous is a dubious translation:
+lean 3 declaration is
+  forall {f : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))}, (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (coeFn.{1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Real -> Complex) (RingHom.hasCoeToFun.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f)) -> (Eq.{1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) f Complex.ofReal)
+but is expected to have type
+  forall {f : RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)}, (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) f)) -> (Eq.{1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) f Complex.ofReal)
+Case conversion may be inaccurate. Consider using '#align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuousₓ'. -/
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
 theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) : f = Complex.ofReal :=
   by
@@ -410,16 +778,34 @@ theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) :
   ext1; rfl
 #align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuous
 
+/- warning: complex.of_real_clm -> Complex.ofRealClm is a dubious translation:
+lean 3 declaration is
+  ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)
+but is expected to have type
+  ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_clm Complex.ofRealClmₓ'. -/
 /-- Continuous linear map version of the canonical embedding of `ℝ` in `ℂ`. -/
 def ofRealClm : ℝ →L[ℝ] ℂ :=
   ofRealLi.toContinuousLinearMap
 #align complex.of_real_clm Complex.ofRealClm
 
+/- warning: complex.of_real_clm_coe -> Complex.ofRealClm_coe is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (HasLiftT.mk.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (CoeTCₓ.coe.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (coeBase.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.addCommMonoid (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (ContinuousLinearMap.LinearMap.coe.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module))))) Complex.ofRealClm) (AlgHom.toLinearMap.{0, 0, 0} Real Real Complex Real.commSemiring Real.semiring (Ring.toSemiring.{0} Complex Complex.ring) (Algebra.id.{0} Real Real.commSemiring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) Complex.ofRealAm)
+but is expected to have type
+  Eq.{1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real Complex Real.instAddCommMonoidReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (ContinuousLinearMap.toLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Complex.ofRealClm) (AlgHom.toLinearMap.{0, 0, 0} Real Real Complex Real.instCommSemiringReal Real.semiring Complex.instSemiringComplex (Algebra.id.{0} Real Real.instCommSemiringReal) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) Complex.ofRealAm)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_clm_coe Complex.ofRealClm_coeₓ'. -/
 @[simp]
 theorem ofRealClm_coe : (ofRealClm : ℝ →ₗ[ℝ] ℂ) = ofRealAm.toLinearMap :=
   rfl
 #align complex.of_real_clm_coe Complex.ofRealClm_coe
 
+/- warning: complex.of_real_clm_apply -> Complex.ofRealClm_apply is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} Complex (coeFn.{1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) (fun (_x : ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) => Real -> Complex) (ContinuousLinearMap.toFun.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.module (Complex.module.{0} Real Real.semiring Real.module)) Complex.ofRealClm x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)
+but is expected to have type
+  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Complex) x) (FunLike.coe.{1, 1, 1} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (ContinuousLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))) Complex.ofRealClm x) (Complex.ofReal' x)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_clm_apply Complex.ofRealClm_applyₓ'. -/
 @[simp]
 theorem ofRealClm_apply (x : ℝ) : ofRealClm x = x :=
   rfl
@@ -451,10 +837,22 @@ noncomputable instance : IsROrC ℂ
       Complex.norm_eq_abs]
   mul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.I_im]
 
+/- warning: is_R_or_C.re_eq_complex_re -> IsROrC.re_eq_complex_re is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Complex -> Real) (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{0} Complex Complex.isROrC)) Complex.re
+but is expected to have type
+  Eq.{1} (forall (ᾰ : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{0} Complex Complex.instIsROrCComplex)) Complex.re
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_complex_re IsROrC.re_eq_complex_reₓ'. -/
 theorem IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
   rfl
 #align is_R_or_C.re_eq_complex_re IsROrC.re_eq_complex_re
 
+/- warning: is_R_or_C.im_eq_complex_im -> IsROrC.im_eq_complex_im is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Complex -> Real) (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{0} Complex Complex.isROrC)) Complex.im
+but is expected to have type
+  Eq.{1} (forall (ᾰ : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{0} Complex Complex.instIsROrCComplex)) Complex.im
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_complex_im IsROrC.im_eq_complex_imₓ'. -/
 theorem IsROrC.im_eq_complex_im : ⇑(IsROrC.im : ℂ →+ ℝ) = Complex.im :=
   rfl
 #align is_R_or_C.im_eq_complex_im IsROrC.im_eq_complex_im
@@ -463,6 +861,12 @@ section ComplexOrder
 
 open ComplexOrder
 
+/- warning: complex.eq_coe_norm_of_nonneg -> Complex.eq_coe_norm_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Norm.norm.{0} Complex Complex.hasNorm z)))
+but is expected to have type
+  forall {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) z) -> (Eq.{1} Complex z (Complex.ofReal' (Norm.norm.{0} Complex Complex.instNormComplex z)))
+Case conversion may be inaccurate. Consider using '#align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonnegₓ'. -/
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
   rw [eq_re_of_real_le hz, IsROrC.norm_ofReal, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
@@ -487,21 +891,45 @@ local notation "IC" => @IsROrC.i ℂ _
 -- mathport name: exprnorm_sqC
 local notation "norm_sqC" => @IsROrC.normSq ℂ _
 
+/- warning: is_R_or_C.re_to_complex -> IsROrC.re_to_complex is a dubious translation:
+lean 3 declaration is
+  forall {x : Complex}, Eq.{1} Real (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{0} Complex Complex.isROrC) x) (Complex.re x)
+but is expected to have type
+  forall {x : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{0} Complex Complex.instIsROrCComplex) x) (Complex.re x)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_to_complex IsROrC.re_to_complexₓ'. -/
 @[simp]
 theorem re_to_complex {x : ℂ} : reC x = x.re :=
   rfl
 #align is_R_or_C.re_to_complex IsROrC.re_to_complex
 
+/- warning: is_R_or_C.im_to_complex -> IsROrC.im_to_complex is a dubious translation:
+lean 3 declaration is
+  forall {x : Complex}, Eq.{1} Real (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex (AddCommGroupWithOne.toAddGroupWithOne.{0} Complex (Ring.toAddCommGroupWithOne.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{0} Complex Complex.isROrC) x) (Complex.im x)
+but is expected to have type
+  forall {x : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonUnitalSemiring.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex (Field.toCommRing.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{0} Complex Complex.instIsROrCComplex) x) (Complex.im x)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_to_complex IsROrC.im_to_complexₓ'. -/
 @[simp]
 theorem im_to_complex {x : ℂ} : imC x = x.im :=
   rfl
 #align is_R_or_C.im_to_complex IsROrC.im_to_complex
 
+/- warning: is_R_or_C.I_to_complex -> IsROrC.I_to_complex is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (IsROrC.i.{0} Complex Complex.isROrC) Complex.I
+but is expected to have type
+  Eq.{1} Complex (IsROrC.I.{0} Complex Complex.instIsROrCComplex) Complex.I
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_to_complex IsROrC.I_to_complexₓ'. -/
 @[simp]
-theorem i_to_complex : IC = Complex.I :=
+theorem I_to_complex : IC = Complex.I :=
   rfl
-#align is_R_or_C.I_to_complex IsROrC.i_to_complex
-
+#align is_R_or_C.I_to_complex IsROrC.I_to_complex
+
+/- warning: is_R_or_C.norm_sq_to_complex -> IsROrC.normSq_to_complex is a dubious translation:
+lean 3 declaration is
+  forall {x : Complex}, Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex (NormedRing.toRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{0} Complex Complex.isROrC) x) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x)
+but is expected to have type
+  forall {x : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex (NormedField.toField.{0} Complex (DenselyNormedField.toNormedField.{0} Complex (IsROrC.toDenselyNormedField.{0} Complex Complex.instIsROrCComplex)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{0} Complex Complex.instIsROrCComplex) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq x)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complexₓ'. -/
 @[simp]
 theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x :=
   rfl
@@ -511,15 +939,33 @@ section tsum
 
 variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]
 
+/- warning: is_R_or_C.has_sum_conj -> IsROrC.hasSum_conj is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) x) (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x))
+but is expected to have type
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) x) (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_conj IsROrC.hasSum_conjₓ'. -/
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
   conjCle.HasSum
 #align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
 
+/- warning: is_R_or_C.has_sum_conj' -> IsROrC.hasSum_conj' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x)) (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x)
+but is expected to have type
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) x)) (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'ₓ'. -/
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   conjCle.hasSum'
 #align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
 
+/- warning: is_R_or_C.summable_conj -> IsROrC.summable_conj is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, Iff (Summable.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x))) (Summable.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f)
+but is expected to have type
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, Iff (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (x : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f x))) (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.summable_conj IsROrC.summable_conjₓ'. -/
 @[simp]
 theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Summable f :=
   summable_star_iff
@@ -527,52 +973,94 @@ theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Sum
 
 variable {𝕜}
 
+/- warning: is_R_or_C.conj_tsum -> IsROrC.conj_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : IsROrC.{u2} 𝕜] (f : α -> 𝕜), Eq.{succ u2} 𝕜 (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (tsum.{u2, u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{u2, u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => coeFn.{succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f a)))
+but is expected to have type
+  forall {α : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : IsROrC.{u2} 𝕜] (f : α -> 𝕜), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (f a)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_tsum IsROrC.conj_tsumₓ'. -/
 theorem conj_tsum (f : α → 𝕜) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   tsum_star
 #align is_R_or_C.conj_tsum IsROrC.conj_tsum
 
 variable (𝕜)
 
+#print IsROrC.hasSum_ofReal /-
 @[simp, norm_cast]
-theorem hasSum_of_real {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : 𝕜)) x ↔ HasSum f x :=
+theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : 𝕜)) x ↔ HasSum f x :=
   ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using re_clm.has_sum h,
     ofRealClm.HasSum⟩
-#align is_R_or_C.has_sum_of_real IsROrC.hasSum_of_real
+#align is_R_or_C.has_sum_of_real IsROrC.hasSum_ofReal
+-/
 
+#print IsROrC.summable_ofReal /-
 @[simp, norm_cast]
-theorem summable_of_real {f : α → ℝ} : (Summable fun x => (f x : 𝕜)) ↔ Summable f :=
+theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : 𝕜)) ↔ Summable f :=
   ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using re_clm.summable h,
     ofRealClm.Summable⟩
-#align is_R_or_C.summable_of_real IsROrC.summable_of_real
+#align is_R_or_C.summable_of_real IsROrC.summable_ofReal
+-/
 
+#print IsROrC.ofReal_tsum /-
 @[norm_cast]
-theorem of_real_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, f a :=
+theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, f a :=
   by
   by_cases h : Summable f
   · exact ContinuousLinearMap.map_tsum of_real_clm h
   ·
     rw [tsum_eq_zero_of_not_summable h,
       tsum_eq_zero_of_not_summable ((summable_of_real _).Not.mpr h), of_real_zero]
-#align is_R_or_C.of_real_tsum IsROrC.of_real_tsum
+#align is_R_or_C.of_real_tsum IsROrC.ofReal_tsum
+-/
 
+/- warning: is_R_or_C.has_sum_re -> IsROrC.hasSum_re is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x) -> (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u2} 𝕜 _inst_1) (f x)) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u2} 𝕜 _inst_1) x))
+but is expected to have type
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x) -> (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) (f x)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) x))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_re IsROrC.hasSum_reₓ'. -/
 theorem hasSum_re {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => re (f x)) (re x) :=
   reClm.HasSum h
 #align is_R_or_C.has_sum_re IsROrC.hasSum_re
 
+/- warning: is_R_or_C.has_sum_im -> IsROrC.hasSum_im is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x) -> (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u2} 𝕜 _inst_1) (f x)) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u2} 𝕜 _inst_1) x))
+but is expected to have type
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜} {x : 𝕜}, (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f x) -> (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u2} 𝕜 _inst_1) (f x)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u2} 𝕜 _inst_1) x))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_im IsROrC.hasSum_imₓ'. -/
 theorem hasSum_im {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => im (f x)) (im x) :=
   imClm.HasSum h
 #align is_R_or_C.has_sum_im IsROrC.hasSum_im
 
+/- warning: is_R_or_C.re_tsum -> IsROrC.re_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, (Summable.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f) -> (Eq.{1} Real (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u2} 𝕜 _inst_1) (tsum.{u2, u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u2} 𝕜 _inst_1) (f a))))
+but is expected to have type
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) (f a))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_tsum IsROrC.re_tsumₓ'. -/
 theorem re_tsum {f : α → 𝕜} (h : Summable f) : re (∑' a, f a) = ∑' a, re (f a) :=
   reClm.map_tsum h
 #align is_R_or_C.re_tsum IsROrC.re_tsum
 
+/- warning: is_R_or_C.im_tsum -> IsROrC.im_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, (Summable.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f) -> (Eq.{1} Real (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u2} 𝕜 _inst_1) (tsum.{u2, u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u2} 𝕜 _inst_1) (f a))))
+but is expected to have type
+  forall {α : Type.{u1}} (𝕜 : Type.{u2}) [_inst_1 : IsROrC.{u2} 𝕜] {f : α -> 𝕜}, (Summable.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u2} 𝕜 _inst_1) (tsum.{u2, u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u2} 𝕜 _inst_1) (f a))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_tsum IsROrC.im_tsumₓ'. -/
 theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a, im (f a) :=
   imClm.map_tsum h
 #align is_R_or_C.im_tsum IsROrC.im_tsum
 
 variable {𝕜}
 
+/- warning: is_R_or_C.has_sum_iff -> IsROrC.hasSum_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : IsROrC.{u2} 𝕜] (f : α -> 𝕜) (c : 𝕜), Iff (HasSum.{u2, u1} 𝕜 α (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f c) (And (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u2} 𝕜 _inst_1) (f x)) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u2} 𝕜 _inst_1) c)) (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u2} 𝕜 _inst_1) (f x)) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => 𝕜 -> Real) (AddMonoidHom.hasCoeToFun.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddMonoidWithOne.toAddMonoid.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u2} 𝕜 _inst_1) c)))
+but is expected to have type
+  forall {α : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : IsROrC.{u2} 𝕜] (f : α -> 𝕜) (c : 𝕜), Iff (HasSum.{u2, u1} 𝕜 α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) f c) (And (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) (f x)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u2} 𝕜 _inst_1) c)) (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u2} 𝕜 _inst_1) (f x)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : 𝕜) => Real) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddZeroClass.toAdd.{u2} 𝕜 (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u2, 0} 𝕜 Real (AddMonoid.toAddZeroClass.{u2} 𝕜 (AddCommMonoid.toAddMonoid.{u2} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonUnitalSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (CommRing.toRing.{u2} 𝕜 (Field.toCommRing.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u2} 𝕜 _inst_1) c)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.has_sum_iff IsROrC.hasSum_iffₓ'. -/
 theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
     HasSum f c ↔ HasSum (fun x => re (f x)) (re c) ∧ HasSum (fun x => im (f x)) (im c) :=
   by
@@ -604,55 +1092,127 @@ variable {α : Type _}
 
 open ComplexConjugate
 
+/- warning: complex.has_sum_conj -> Complex.hasSum_conj is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x)) x) (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x))
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x)) x) (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x))
+Case conversion may be inaccurate. Consider using '#align complex.has_sum_conj Complex.hasSum_conjₓ'. -/
 @[simp]
 theorem hasSum_conj {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
   IsROrC.hasSum_conj _
 #align complex.has_sum_conj Complex.hasSum_conj
 
+/- warning: complex.has_sum_conj' -> Complex.hasSum_conj' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x)) (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f x)
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x)) (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f x)
+Case conversion may be inaccurate. Consider using '#align complex.has_sum_conj' Complex.hasSum_conj'ₓ'. -/
 theorem hasSum_conj' {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   IsROrC.hasSum_conj' _
 #align complex.has_sum_conj' Complex.hasSum_conj'
 
+/- warning: complex.summable_conj -> Complex.summable_conj is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Complex}, Iff (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f x))) (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f)
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Complex}, Iff (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f x))) (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f)
+Case conversion may be inaccurate. Consider using '#align complex.summable_conj Complex.summable_conjₓ'. -/
 @[simp]
 theorem summable_conj {f : α → ℂ} : (Summable fun x => conj (f x)) ↔ Summable f :=
   IsROrC.summable_conj _
 #align complex.summable_conj Complex.summable_conj
 
+/- warning: complex.conj_tsum -> Complex.conj_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (f : α -> Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (tsum.{0, u1} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) α (fun (a : α) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (f a)))
+but is expected to have type
+  forall {α : Type.{u1}} (f : α -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (f a)))
+Case conversion may be inaccurate. Consider using '#align complex.conj_tsum Complex.conj_tsumₓ'. -/
 theorem conj_tsum (f : α → ℂ) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   IsROrC.conj_tsum _
 #align complex.conj_tsum Complex.conj_tsum
 
+/- warning: complex.has_sum_of_real -> Complex.hasSum_ofReal is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Real} {x : Real}, Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (f x)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x)
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Real} {x : Real}, Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => Complex.ofReal' (f x)) (Complex.ofReal' x)) (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x)
+Case conversion may be inaccurate. Consider using '#align complex.has_sum_of_real Complex.hasSum_ofRealₓ'. -/
 @[simp, norm_cast]
-theorem hasSum_of_real {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : ℂ)) x ↔ HasSum f x :=
-  IsROrC.hasSum_of_real _
-#align complex.has_sum_of_real Complex.hasSum_of_real
-
+theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : ℂ)) x ↔ HasSum f x :=
+  IsROrC.hasSum_ofReal _
+#align complex.has_sum_of_real Complex.hasSum_ofReal
+
+/- warning: complex.summable_of_real -> Complex.summable_ofReal is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Real}, Iff (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (f x))) (Summable.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f)
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Real}, Iff (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => Complex.ofReal' (f x))) (Summable.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f)
+Case conversion may be inaccurate. Consider using '#align complex.summable_of_real Complex.summable_ofRealₓ'. -/
 @[simp, norm_cast]
-theorem summable_of_real {f : α → ℝ} : (Summable fun x => (f x : ℂ)) ↔ Summable f :=
-  IsROrC.summable_of_real _
-#align complex.summable_of_real Complex.summable_of_real
-
+theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : ℂ)) ↔ Summable f :=
+  IsROrC.summable_ofReal _
+#align complex.summable_of_real Complex.summable_ofReal
+
+/- warning: complex.of_real_tsum -> Complex.ofReal_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (f : α -> Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) α (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (f a)))
+but is expected to have type
+  forall {α : Type.{u1}} (f : α -> Real), Eq.{1} Complex (Complex.ofReal' (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => f a))) (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => Complex.ofReal' (f a)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_tsum Complex.ofReal_tsumₓ'. -/
 @[norm_cast]
-theorem of_real_tsum (f : α → ℝ) : (↑(∑' a, f a) : ℂ) = ∑' a, f a :=
-  IsROrC.of_real_tsum _ _
-#align complex.of_real_tsum Complex.of_real_tsum
-
+theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : ℂ) = ∑' a, f a :=
+  IsROrC.ofReal_tsum _ _
+#align complex.of_real_tsum Complex.ofReal_tsum
+
+/- warning: complex.has_sum_re -> Complex.hasSum_re is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f x) -> (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.re (f x)) (Complex.re x))
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f x) -> (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.re (f x)) (Complex.re x))
+Case conversion may be inaccurate. Consider using '#align complex.has_sum_re Complex.hasSum_reₓ'. -/
 theorem hasSum_re {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).re) x.re :=
   IsROrC.hasSum_re _ h
 #align complex.has_sum_re Complex.hasSum_re
 
+/- warning: complex.has_sum_im -> Complex.hasSum_im is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f x) -> (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.im (f x)) (Complex.im x))
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Complex} {x : Complex}, (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f x) -> (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.im (f x)) (Complex.im x))
+Case conversion may be inaccurate. Consider using '#align complex.has_sum_im Complex.hasSum_imₓ'. -/
 theorem hasSum_im {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).im) x.im :=
   IsROrC.hasSum_im _ h
 #align complex.has_sum_im Complex.hasSum_im
 
+/- warning: complex.re_tsum -> Complex.re_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Complex}, (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f) -> (Eq.{1} Real (Complex.re (tsum.{0, u1} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => Complex.re (f a))))
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Complex}, (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f) -> (Eq.{1} Real (Complex.re (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => Complex.re (f a))))
+Case conversion may be inaccurate. Consider using '#align complex.re_tsum Complex.re_tsumₓ'. -/
 theorem re_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).re = ∑' a, (f a).re :=
   IsROrC.re_tsum _ h
 #align complex.re_tsum Complex.re_tsum
 
+/- warning: complex.im_tsum -> Complex.im_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : α -> Complex}, (Summable.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f) -> (Eq.{1} Real (Complex.im (tsum.{0, u1} Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => Complex.im (f a))))
+but is expected to have type
+  forall {α : Type.{u1}} {f : α -> Complex}, (Summable.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f) -> (Eq.{1} Real (Complex.im (tsum.{0, u1} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) α (fun (a : α) => f a))) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) α (fun (a : α) => Complex.im (f a))))
+Case conversion may be inaccurate. Consider using '#align complex.im_tsum Complex.im_tsumₓ'. -/
 theorem im_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).im = ∑' a, (f a).im :=
   IsROrC.im_tsum _ h
 #align complex.im_tsum Complex.im_tsum
 
+/- warning: complex.has_sum_iff -> Complex.hasSum_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (f : α -> Complex) (c : Complex), Iff (HasSum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f c) (And (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.re (f x)) (Complex.re c)) (HasSum.{0, u1} Real α Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.im (f x)) (Complex.im c)))
+but is expected to have type
+  forall {α : Type.{u1}} (f : α -> Complex) (c : Complex), Iff (HasSum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f c) (And (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.re (f x)) (Complex.re c)) (HasSum.{0, u1} Real α Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => Complex.im (f x)) (Complex.im c)))
+Case conversion may be inaccurate. Consider using '#align complex.has_sum_iff Complex.hasSum_iffₓ'. -/
 theorem hasSum_iff (f : α → ℂ) (c : ℂ) :
     HasSum f c ↔ HasSum (fun x => (f x).re) c.re ∧ HasSum (fun x => (f x).im) c.im :=
   IsROrC.hasSum_iff _ _

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -464,7 +464,7 @@ section ComplexOrder
 open ComplexOrder
 
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
-  rw [eq_re_of_real_le hz, IsROrC.norm_of_real, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
+  rw [eq_re_of_real_le hz, IsROrC.norm_ofReal, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
 
 end ComplexOrder
@@ -535,13 +535,13 @@ variable (𝕜)
 
 @[simp, norm_cast]
 theorem hasSum_of_real {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : 𝕜)) x ↔ HasSum f x :=
-  ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.of_real_re] using re_clm.has_sum h,
+  ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using re_clm.has_sum h,
     ofRealClm.HasSum⟩
 #align is_R_or_C.has_sum_of_real IsROrC.hasSum_of_real
 
 @[simp, norm_cast]
 theorem summable_of_real {f : α → ℝ} : (Summable fun x => (f x : 𝕜)) ↔ Summable f :=
-  ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.of_real_re] using re_clm.summable h,
+  ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using re_clm.summable h,
     ofRealClm.Summable⟩
 #align is_R_or_C.summable_of_real IsROrC.summable_of_real
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.complex.basic
-! leanprover-community/mathlib commit 338fe44f54751b9f7deaca47ffca3509f53140ae
+! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -464,7 +464,7 @@ section ComplexOrder
 open ComplexOrder
 
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
-  rw [eq_re_of_real_le hz, IsROrC.norm_of_real, Real.norm_of_nonneg (Complex.le_def.2 hz).1]
+  rw [eq_re_of_real_le hz, IsROrC.norm_of_real, _root_.abs_of_nonneg (Complex.le_def.2 hz).1]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
 
 end ComplexOrder
@@ -484,9 +484,6 @@ local notation "imC" => @IsROrC.im ℂ _
 -- mathport name: exprIC
 local notation "IC" => @IsROrC.i ℂ _
 
--- mathport name: exprabsC
-local notation "absC" => @IsROrC.abs ℂ _
-
 -- mathport name: exprnorm_sqC
 local notation "norm_sqC" => @IsROrC.normSq ℂ _
 
@@ -506,14 +503,10 @@ theorem i_to_complex : IC = Complex.I :=
 #align is_R_or_C.I_to_complex IsROrC.i_to_complex
 
 @[simp]
-theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x := by
-  simp [IsROrC.normSq, Complex.normSq]
+theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x :=
+  rfl
 #align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complex
 
-@[simp]
-theorem abs_to_complex {x : ℂ} : absC x = Complex.abs x := by simp [IsROrC.abs, Complex.abs]
-#align is_R_or_C.abs_to_complex IsROrC.abs_to_complex
-
 section tsum
 
 variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.complex.basic
-! leanprover-community/mathlib commit 32253a1a1071173b33dc7d6a218cf722c6feb514
+! leanprover-community/mathlib commit 338fe44f54751b9f7deaca47ffca3509f53140ae
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -450,10 +450,6 @@ noncomputable instance : IsROrC ℂ
     simp only [← Complex.normSq_eq_abs, ← Complex.normSq_apply, AddMonoidHom.coe_mk,
       Complex.norm_eq_abs]
   mul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.I_im]
-  inv_def_ax z := by
-    simp only [Complex.inv_def, Complex.normSq_eq_abs, Complex.coe_algebraMap,
-      Complex.ofReal_eq_coe, Complex.norm_eq_abs]
-  div_i_ax := Complex.div_I
 
 theorem IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
   rfl

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

@@ -38,7 +38,7 @@ We also register the fact that `ℂ` is an `is_R_or_C` field.
 -/
 
 
-assert_not_exists absorbs
+assert_not_exists Absorbs
 
 noncomputable section
 
@@ -83,7 +83,7 @@ instance {R : Type _} [NormedField R] [NormedAlgebra R ℝ] : NormedAlgebra R 
   norm_smul_le r x :=
     by
     rw [norm_eq_abs, norm_eq_abs, ← algebraMap_smul ℝ r x, Algebra.smul_def, map_mul, ←
-      norm_algebra_map' ℝ r, coe_algebra_map, abs_of_real]
+      norm_algebraMap' ℝ r, coe_algebra_map, abs_of_real]
     rfl
   toAlgebra := Complex.algebra
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -528,7 +528,7 @@ theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x))
 #align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
 
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
-  conjCle.has_sum'
+  conjCle.hasSum'
 #align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

@@ -468,8 +468,7 @@ section ComplexOrder
 open ComplexOrder
 
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
-  rw [eq_re_of_real_le hz, IsROrC.norm_of_real,
-    Real.norm_of_nonneg (Complex.ComplexOrder.le_def.2 hz).1]
+  rw [eq_re_of_real_le hz, IsROrC.norm_of_real, Real.norm_of_nonneg (Complex.le_def.2 hz).1]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
 
 end ComplexOrder

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

@@ -405,8 +405,7 @@ theorem continuous_of_real : Continuous (coe : ℝ → ℂ) :=
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
 theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) : f = Complex.ofReal :=
   by
-  convert
-    congr_arg AlgHom.toRingHom
+  convert congr_arg AlgHom.toRingHom
       (Subsingleton.elim (AlgHom.mk' f <| map_real_smul f h) <| Algebra.ofId ℝ ℂ)
   ext1; rfl
 #align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuous
@@ -592,7 +591,7 @@ theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
   refine' ⟨fun h => ⟨has_sum_re _ h, has_sum_im _ h⟩, _⟩
   rintro ⟨h₁, h₂⟩
   rw [← IsROrC.re_add_im c]
-  convert ((has_sum_of_real 𝕜).mpr h₁).add (((has_sum_of_real 𝕜).mpr h₂).mul_right I)
+  convert((has_sum_of_real 𝕜).mpr h₁).add (((has_sum_of_real 𝕜).mpr h₂).mul_right I)
   simp_rw [IsROrC.re_add_im]
 #align is_R_or_C.has_sum_iff IsROrC.hasSum_iff
 

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

@@ -47,10 +47,10 @@ namespace Complex
 open ComplexConjugate Topology
 
 instance : Norm ℂ :=
-  ⟨Complex.AbsTheory.Complex.abs⟩
+  ⟨abs⟩
 
 @[simp]
-theorem norm_eq_abs (z : ℂ) : ‖z‖ = Complex.AbsTheory.Complex.abs z :=
+theorem norm_eq_abs (z : ℂ) : ‖z‖ = abs z :=
   rfl
 #align complex.norm_eq_abs Complex.norm_eq_abs
 
@@ -60,18 +60,17 @@ theorem norm_exp_of_real_mul_i (t : ℝ) : ‖exp (t * I)‖ = 1 := by
 
 instance : NormedAddCommGroup ℂ :=
   AddGroupNorm.toNormedAddCommGroup
-    {
-      Complex.AbsTheory.Complex.abs with
-      map_zero' := map_zero Complex.AbsTheory.Complex.abs
-      neg' := Complex.AbsTheory.Complex.abs.map_neg
-      eq_zero_of_map_eq_zero' := fun _ => Complex.AbsTheory.Complex.abs.eq_zero.1 }
+    { abs with
+      map_zero' := map_zero abs
+      neg' := abs.map_neg
+      eq_zero_of_map_eq_zero' := fun _ => abs.eq_zero.1 }
 
 instance : NormedField ℂ :=
   { Complex.field,
     Complex.normedAddCommGroup with
-    norm := Complex.AbsTheory.Complex.abs
+    norm := abs
     dist_eq := fun _ _ => rfl
-    norm_mul' := map_mul Complex.AbsTheory.Complex.abs }
+    norm_mul' := map_mul abs }
 
 instance : DenselyNormedField ℂ
     where lt_norm_lt r₁ r₂ h₀ hr :=
@@ -96,7 +95,7 @@ instance (priority := 900) NormedSpace.complexToReal : NormedSpace ℝ E :=
   NormedSpace.restrictScalars ℝ ℂ E
 #align normed_space.complex_to_real NormedSpace.complexToReal
 
-theorem dist_eq (z w : ℂ) : dist z w = Complex.AbsTheory.Complex.abs (z - w) :=
+theorem dist_eq (z w : ℂ) : dist z w = abs (z - w) :=
   rfl
 #align complex.dist_eq Complex.dist_eq
 
@@ -153,7 +152,7 @@ theorem nndist_self_conj (z : ℂ) : nndist z (conj z) = 2 * Real.nnabs z.im :=
 #align complex.nndist_self_conj Complex.nndist_self_conj
 
 @[simp]
-theorem comap_abs_nhds_zero : Filter.comap Complex.AbsTheory.Complex.abs (𝓝 0) = 𝓝 0 :=
+theorem comap_abs_nhds_zero : Filter.comap abs (𝓝 0) = 𝓝 0 :=
   comap_norm_nhds_zero
 #align complex.comap_abs_nhds_zero Complex.comap_abs_nhds_zero
 
@@ -182,7 +181,7 @@ theorem norm_int_of_nonneg {n : ℤ} (hn : 0 ≤ n) : ‖(n : ℂ)‖ = n := by
 #align complex.norm_int_of_nonneg Complex.norm_int_of_nonneg
 
 @[continuity]
-theorem continuous_abs : Continuous Complex.AbsTheory.Complex.abs :=
+theorem continuous_abs : Continuous abs :=
   continuous_norm
 #align complex.continuous_abs Complex.continuous_abs
 
@@ -216,12 +215,12 @@ theorem norm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n
   congr_arg coe (nnnorm_eq_one_of_pow_eq_one h hn)
 #align complex.norm_eq_one_of_pow_eq_one Complex.norm_eq_one_of_pow_eq_one
 
-theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ Complex.AbsTheory.Complex.abs z := by
+theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ abs z := by
   simp [Prod.norm_def, abs_re_le_abs, abs_im_le_abs]
 #align complex.equiv_real_prod_apply_le Complex.equivRealProd_apply_le
 
-theorem equivRealProd_apply_le' (z : ℂ) : ‖equivRealProd z‖ ≤ 1 * Complex.AbsTheory.Complex.abs z :=
-  by simpa using equiv_real_prod_apply_le z
+theorem equivRealProd_apply_le' (z : ℂ) : ‖equivRealProd z‖ ≤ 1 * abs z := by
+  simpa using equiv_real_prod_apply_le z
 #align complex.equiv_real_prod_apply_le' Complex.equivRealProd_apply_le'
 
 theorem lipschitz_equivRealProd : LipschitzWith 1 equivRealProd := by
@@ -250,8 +249,7 @@ instance : ProperSpace ℂ :=
   (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdClm.toHomeomorph).ProperSpace
 
 /-- The `abs` function on `ℂ` is proper. -/
-theorem tendsto_abs_cocompact_atTop :
-    Filter.Tendsto Complex.AbsTheory.Complex.abs (Filter.cocompact ℂ) Filter.atTop :=
+theorem tendsto_abs_cocompact_atTop : Filter.Tendsto abs (Filter.cocompact ℂ) Filter.atTop :=
   tendsto_norm_cocompact_atTop
 #align complex.tendsto_abs_cocompact_at_top Complex.tendsto_abs_cocompact_atTop
 
@@ -433,8 +431,8 @@ noncomputable instance : IsROrC ℂ
   re := ⟨Complex.re, Complex.zero_re, Complex.add_re⟩
   im := ⟨Complex.im, Complex.zero_im, Complex.add_im⟩
   I := Complex.I
-  i_re_ax := by simp only [AddMonoidHom.coe_mk, Complex.i_re]
-  i_mul_i_ax := by simp only [Complex.i_mul_I, eq_self_iff_true, or_true_iff]
+  i_re_ax := by simp only [AddMonoidHom.coe_mk, Complex.I_re]
+  i_mul_i_ax := by simp only [Complex.I_mul_I, eq_self_iff_true, or_true_iff]
   re_add_im_ax z := by
     simp only [AddMonoidHom.coe_mk, Complex.re_add_im, Complex.coe_algebraMap,
       Complex.ofReal_eq_coe]
@@ -452,7 +450,7 @@ noncomputable instance : IsROrC ℂ
   norm_sq_eq_def_ax z := by
     simp only [← Complex.normSq_eq_abs, ← Complex.normSq_apply, AddMonoidHom.coe_mk,
       Complex.norm_eq_abs]
-  mul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.i_im]
+  mul_im_i_ax z := by simp only [mul_one, AddMonoidHom.coe_mk, Complex.I_im]
   inv_def_ax z := by
     simp only [Complex.inv_def, Complex.normSq_eq_abs, Complex.coe_algebraMap,
       Complex.ofReal_eq_coe, Complex.norm_eq_abs]
@@ -519,8 +517,7 @@ theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x := by
 #align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complex
 
 @[simp]
-theorem abs_to_complex {x : ℂ} : absC x = Complex.AbsTheory.Complex.abs x := by
-  simp [IsROrC.abs, Complex.AbsTheory.Complex.abs]
+theorem abs_to_complex {x : ℂ} : absC x = Complex.abs x := by simp [IsROrC.abs, Complex.abs]
 #align is_R_or_C.abs_to_complex IsROrC.abs_to_complex
 
 section tsum

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

@@ -47,30 +47,31 @@ namespace Complex
 open ComplexConjugate Topology
 
 instance : Norm ℂ :=
-  ⟨abs⟩
+  ⟨Complex.AbsTheory.Complex.abs⟩
 
 @[simp]
-theorem norm_eq_abs (z : ℂ) : ‖z‖ = abs z :=
+theorem norm_eq_abs (z : ℂ) : ‖z‖ = Complex.AbsTheory.Complex.abs z :=
   rfl
 #align complex.norm_eq_abs Complex.norm_eq_abs
 
-theorem norm_exp_of_real_mul_i (t : ℝ) : ‖exp (t * i)‖ = 1 := by
+theorem norm_exp_of_real_mul_i (t : ℝ) : ‖exp (t * I)‖ = 1 := by
   simp only [norm_eq_abs, abs_exp_of_real_mul_I]
 #align complex.norm_exp_of_real_mul_I Complex.norm_exp_of_real_mul_i
 
 instance : NormedAddCommGroup ℂ :=
   AddGroupNorm.toNormedAddCommGroup
-    { abs with
-      map_zero' := map_zero abs
-      neg' := abs.map_neg
-      eq_zero_of_map_eq_zero' := fun _ => abs.eq_zero.1 }
+    {
+      Complex.AbsTheory.Complex.abs with
+      map_zero' := map_zero Complex.AbsTheory.Complex.abs
+      neg' := Complex.AbsTheory.Complex.abs.map_neg
+      eq_zero_of_map_eq_zero' := fun _ => Complex.AbsTheory.Complex.abs.eq_zero.1 }
 
 instance : NormedField ℂ :=
   { Complex.field,
     Complex.normedAddCommGroup with
-    norm := abs
+    norm := Complex.AbsTheory.Complex.abs
     dist_eq := fun _ _ => rfl
-    norm_mul' := map_mul abs }
+    norm_mul' := map_mul Complex.AbsTheory.Complex.abs }
 
 instance : DenselyNormedField ℂ
     where lt_norm_lt r₁ r₂ h₀ hr :=
@@ -95,7 +96,7 @@ instance (priority := 900) NormedSpace.complexToReal : NormedSpace ℝ E :=
   NormedSpace.restrictScalars ℝ ℂ E
 #align normed_space.complex_to_real NormedSpace.complexToReal
 
-theorem dist_eq (z w : ℂ) : dist z w = abs (z - w) :=
+theorem dist_eq (z w : ℂ) : dist z w = Complex.AbsTheory.Complex.abs (z - w) :=
   rfl
 #align complex.dist_eq Complex.dist_eq
 
@@ -152,12 +153,12 @@ theorem nndist_self_conj (z : ℂ) : nndist z (conj z) = 2 * Real.nnabs z.im :=
 #align complex.nndist_self_conj Complex.nndist_self_conj
 
 @[simp]
-theorem comap_abs_nhds_zero : Filter.comap abs (𝓝 0) = 𝓝 0 :=
+theorem comap_abs_nhds_zero : Filter.comap Complex.AbsTheory.Complex.abs (𝓝 0) = 𝓝 0 :=
   comap_norm_nhds_zero
 #align complex.comap_abs_nhds_zero Complex.comap_abs_nhds_zero
 
 theorem norm_real (r : ℝ) : ‖(r : ℂ)‖ = ‖r‖ :=
-  abs_of_real _
+  abs_ofReal _
 #align complex.norm_real Complex.norm_real
 
 @[simp]
@@ -181,7 +182,7 @@ theorem norm_int_of_nonneg {n : ℤ} (hn : 0 ≤ n) : ‖(n : ℂ)‖ = n := by
 #align complex.norm_int_of_nonneg Complex.norm_int_of_nonneg
 
 @[continuity]
-theorem continuous_abs : Continuous abs :=
+theorem continuous_abs : Continuous Complex.AbsTheory.Complex.abs :=
   continuous_norm
 #align complex.continuous_abs Complex.continuous_abs
 
@@ -215,12 +216,12 @@ theorem norm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n
   congr_arg coe (nnnorm_eq_one_of_pow_eq_one h hn)
 #align complex.norm_eq_one_of_pow_eq_one Complex.norm_eq_one_of_pow_eq_one
 
-theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ abs z := by
+theorem equivRealProd_apply_le (z : ℂ) : ‖equivRealProd z‖ ≤ Complex.AbsTheory.Complex.abs z := by
   simp [Prod.norm_def, abs_re_le_abs, abs_im_le_abs]
 #align complex.equiv_real_prod_apply_le Complex.equivRealProd_apply_le
 
-theorem equivRealProd_apply_le' (z : ℂ) : ‖equivRealProd z‖ ≤ 1 * abs z := by
-  simpa using equiv_real_prod_apply_le z
+theorem equivRealProd_apply_le' (z : ℂ) : ‖equivRealProd z‖ ≤ 1 * Complex.AbsTheory.Complex.abs z :=
+  by simpa using equiv_real_prod_apply_le z
 #align complex.equiv_real_prod_apply_le' Complex.equivRealProd_apply_le'
 
 theorem lipschitz_equivRealProd : LipschitzWith 1 equivRealProd := by
@@ -249,7 +250,8 @@ instance : ProperSpace ℂ :=
   (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdClm.toHomeomorph).ProperSpace
 
 /-- The `abs` function on `ℂ` is proper. -/
-theorem tendsto_abs_cocompact_atTop : Filter.Tendsto abs (Filter.cocompact ℂ) Filter.atTop :=
+theorem tendsto_abs_cocompact_atTop :
+    Filter.Tendsto Complex.AbsTheory.Complex.abs (Filter.cocompact ℂ) Filter.atTop :=
   tendsto_norm_cocompact_atTop
 #align complex.tendsto_abs_cocompact_at_top Complex.tendsto_abs_cocompact_atTop
 
@@ -304,7 +306,7 @@ theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
 
 theorem restrictScalars_one_smul_right' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smul_right x : ℂ →L[ℂ] E) =
-      reClm.smul_right x + i • imClm.smul_right x :=
+      reClm.smul_right x + I • imClm.smul_right x :=
   by
   ext ⟨a, b⟩
   simp [mk_eq_add_mul_I, add_smul, mul_smul, smul_comm I]
@@ -430,23 +432,23 @@ noncomputable instance : IsROrC ℂ
     where
   re := ⟨Complex.re, Complex.zero_re, Complex.add_re⟩
   im := ⟨Complex.im, Complex.zero_im, Complex.add_im⟩
-  i := Complex.i
+  I := Complex.I
   i_re_ax := by simp only [AddMonoidHom.coe_mk, Complex.i_re]
-  i_mul_i_ax := by simp only [Complex.i_mul_i, eq_self_iff_true, or_true_iff]
+  i_mul_i_ax := by simp only [Complex.i_mul_I, eq_self_iff_true, or_true_iff]
   re_add_im_ax z := by
     simp only [AddMonoidHom.coe_mk, Complex.re_add_im, Complex.coe_algebraMap,
       Complex.ofReal_eq_coe]
   of_real_re_ax r := by
-    simp only [AddMonoidHom.coe_mk, Complex.of_real_re, Complex.coe_algebraMap,
+    simp only [AddMonoidHom.coe_mk, Complex.ofReal_re, Complex.coe_algebraMap,
       Complex.ofReal_eq_coe]
   of_real_im_ax r := by
-    simp only [AddMonoidHom.coe_mk, Complex.of_real_im, Complex.coe_algebraMap,
+    simp only [AddMonoidHom.coe_mk, Complex.ofReal_im, Complex.coe_algebraMap,
       Complex.ofReal_eq_coe]
   mul_re_ax z w := by simp only [Complex.mul_re, AddMonoidHom.coe_mk]
   mul_im_ax z w := by simp only [AddMonoidHom.coe_mk, Complex.mul_im]
   conj_re_ax z := rfl
   conj_im_ax z := rfl
-  conj_i_ax := by simp only [Complex.conj_i, RingHom.coe_mk]
+  conj_i_ax := by simp only [Complex.conj_I, RingHom.coe_mk]
   norm_sq_eq_def_ax z := by
     simp only [← Complex.normSq_eq_abs, ← Complex.normSq_apply, AddMonoidHom.coe_mk,
       Complex.norm_eq_abs]
@@ -454,7 +456,7 @@ noncomputable instance : IsROrC ℂ
   inv_def_ax z := by
     simp only [Complex.inv_def, Complex.normSq_eq_abs, Complex.coe_algebraMap,
       Complex.ofReal_eq_coe, Complex.norm_eq_abs]
-  div_i_ax := Complex.div_i
+  div_i_ax := Complex.div_I
 
 theorem IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
   rfl
@@ -469,7 +471,8 @@ section ComplexOrder
 open ComplexOrder
 
 theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
-  rw [eq_re_of_real_le hz, IsROrC.norm_of_real, Real.norm_of_nonneg (Complex.le_def.2 hz).1]
+  rw [eq_re_of_real_le hz, IsROrC.norm_of_real,
+    Real.norm_of_nonneg (Complex.ComplexOrder.le_def.2 hz).1]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
 
 end ComplexOrder
@@ -506,7 +509,7 @@ theorem im_to_complex {x : ℂ} : imC x = x.im :=
 #align is_R_or_C.im_to_complex IsROrC.im_to_complex
 
 @[simp]
-theorem i_to_complex : IC = Complex.i :=
+theorem i_to_complex : IC = Complex.I :=
   rfl
 #align is_R_or_C.I_to_complex IsROrC.i_to_complex
 
@@ -516,7 +519,8 @@ theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x := by
 #align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complex
 
 @[simp]
-theorem abs_to_complex {x : ℂ} : absC x = Complex.abs x := by simp [IsROrC.abs, Complex.abs]
+theorem abs_to_complex {x : ℂ} : absC x = Complex.AbsTheory.Complex.abs x := by
+  simp [IsROrC.abs, Complex.AbsTheory.Complex.abs]
 #align is_R_or_C.abs_to_complex IsROrC.abs_to_complex
 
 section tsum

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -46,7 +46,7 @@ namespace Complex
 
 open ComplexConjugate Topology
 
-instance : HasNorm ℂ :=
+instance : Norm ℂ :=
   ⟨abs⟩
 
 @[simp]

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

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -161,7 +161,7 @@ theorem norm_real (r : ℝ) : ‖(r : ℂ)‖ = ‖r‖ :=
 
 @[simp 1100]
 theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| := by
-  rw [← ofReal_rat_cast]
+  rw [← ofReal_ratCast]
   exact norm_real _
 #align complex.norm_rat Complex.norm_rat
 
@@ -726,12 +726,12 @@ lemma neg_ofReal_mem_slitPlane {x : ℝ} : -↑x ∈ slitPlane ↔ x < 0 := by
 lemma zero_not_mem_slitPlane : 0 ∉ slitPlane := mt ofReal_mem_slitPlane.1 (lt_irrefl _)
 
 @[simp]
-lemma nat_cast_mem_slitPlane {n : ℕ} : ↑n ∈ slitPlane ↔ n ≠ 0 := by
+lemma natCast_mem_slitPlane {n : ℕ} : ↑n ∈ slitPlane ↔ n ≠ 0 := by
   simpa [pos_iff_ne_zero] using @ofReal_mem_slitPlane n
 
 @[simp]
 lemma ofNat_mem_slitPlane (n : ℕ) [n.AtLeastTwo] : no_index (OfNat.ofNat n) ∈ slitPlane :=
-  nat_cast_mem_slitPlane.2 (NeZero.ne n)
+  natCast_mem_slitPlane.2 (NeZero.ne n)
 
 lemma mem_slitPlane_iff_not_le_zero {z : ℂ} : z ∈ slitPlane ↔ ¬z ≤ 0 :=
   mem_slitPlane_iff.trans not_le_zero_iff.symm

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

• Is far more common thatn NNReal.sqrt and Nat.sqrt
• Is far more interesting to mathlib than sqrt on Float
• Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
• Will be replaced by a more general typeclass in a future PR.

Zulip

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -99,14 +99,14 @@ theorem dist_eq (z w : ℂ) : dist z w = abs (z - w) :=
   rfl
 #align complex.dist_eq Complex.dist_eq
 
-theorem dist_eq_re_im (z w : ℂ) : dist z w = Real.sqrt ((z.re - w.re) ^ 2 + (z.im - w.im) ^ 2) := by
+theorem dist_eq_re_im (z w : ℂ) : dist z w = √((z.re - w.re) ^ 2 + (z.im - w.im) ^ 2) := by
   rw [sq, sq]
   rfl
 #align complex.dist_eq_re_im Complex.dist_eq_re_im
 
 @[simp]
 theorem dist_mk (x₁ y₁ x₂ y₂ : ℝ) :
-    dist (mk x₁ y₁) (mk x₂ y₂) = Real.sqrt ((x₁ - x₂) ^ 2 + (y₁ - y₂) ^ 2) :=
+    dist (mk x₁ y₁) (mk x₂ y₂) = √((x₁ - x₂) ^ 2 + (y₁ - y₂) ^ 2) :=
   dist_eq_re_im _ _
 #align complex.dist_mk Complex.dist_mk
 
@@ -243,7 +243,7 @@ instance instT2Space : T2Space ℂ := TopologicalSpace.t2Space_of_metrizableSpac
 /-- The natural `ContinuousLinearEquiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps! (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
 def equivRealProdCLM : ℂ ≃L[ℝ] ℝ × ℝ :=
-  equivRealProdLm.toContinuousLinearEquivOfBounds 1 (Real.sqrt 2) equivRealProd_apply_le' fun p =>
+  equivRealProdLm.toContinuousLinearEquivOfBounds 1 (√2) equivRealProd_apply_le' fun p =>
     abs_le_sqrt_two_mul_max (equivRealProd.symm p)
 #align complex.equiv_real_prod_clm Complex.equivRealProdCLM
 

RCLike is an analytic typeclass, hence should be under Analysis

@@ -6,7 +6,7 @@ Authors: Sébastien Gouëzel
 import Mathlib.Data.Complex.Module
 import Mathlib.Data.Complex.Order
 import Mathlib.Data.Complex.Exponential
-import Mathlib.Data.RCLike.Basic
+import Mathlib.Analysis.RCLike.Basic
 import Mathlib.Topology.Algebra.InfiniteSum.Module
 import Mathlib.Topology.Instances.RealVectorSpace
 

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.

@@ -6,7 +6,7 @@ Authors: Sébastien Gouëzel
 import Mathlib.Data.Complex.Module
 import Mathlib.Data.Complex.Order
 import Mathlib.Data.Complex.Exponential
-import Mathlib.Data.IsROrC.Basic
+import Mathlib.Data.RCLike.Basic
 import Mathlib.Topology.Algebra.InfiniteSum.Module
 import Mathlib.Topology.Instances.RealVectorSpace
 
@@ -32,7 +32,7 @@ They are bundled versions of the real part, the imaginary part, the embedding of
 the complex conjugate as continuous `ℝ`-linear maps. The last two are also bundled as linear
 isometries in `ofRealLI` and `conjLIE`.
 
-We also register the fact that `ℂ` is an `IsROrC` field.
+We also register the fact that `ℂ` is an `RCLike` field.
 -/
 
 
@@ -427,7 +427,7 @@ theorem ofRealCLM_apply (x : ℝ) : ofRealCLM x = x :=
   rfl
 #align complex.of_real_clm_apply Complex.ofRealCLM_apply
 
-noncomputable instance : IsROrC ℂ where
+noncomputable instance : RCLike ℂ where
   re := ⟨⟨Complex.re, Complex.zero_re⟩, Complex.add_re⟩
   im := ⟨⟨Complex.im, Complex.zero_im⟩, Complex.add_im⟩
   I := Complex.I
@@ -446,53 +446,53 @@ noncomputable instance : IsROrC ℂ where
   toPartialOrder := Complex.partialOrder
   le_iff_re_im := Iff.rfl
 
-theorem _root_.IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
+theorem _root_.RCLike.re_eq_complex_re : ⇑(RCLike.re : ℂ →+ ℝ) = Complex.re :=
   rfl
-#align is_R_or_C.re_eq_complex_re IsROrC.re_eq_complex_re
+#align is_R_or_C.re_eq_complex_re RCLike.re_eq_complex_re
 
-theorem _root_.IsROrC.im_eq_complex_im : ⇑(IsROrC.im : ℂ →+ ℝ) = Complex.im :=
+theorem _root_.RCLike.im_eq_complex_im : ⇑(RCLike.im : ℂ →+ ℝ) = Complex.im :=
   rfl
-#align is_R_or_C.im_eq_complex_im IsROrC.im_eq_complex_im
+#align is_R_or_C.im_eq_complex_im RCLike.im_eq_complex_im
 
 -- TODO: Replace `mul_conj` and `conj_mul` once `norm` has replaced `abs`
-lemma mul_conj' (z : ℂ) : z * conj z = ‖z‖ ^ 2 := IsROrC.mul_conj z
-lemma conj_mul' (z : ℂ) : conj z * z = ‖z‖ ^ 2 := IsROrC.conj_mul z
+lemma mul_conj' (z : ℂ) : z * conj z = ‖z‖ ^ 2 := RCLike.mul_conj z
+lemma conj_mul' (z : ℂ) : conj z * z = ‖z‖ ^ 2 := RCLike.conj_mul z
 
-lemma inv_eq_conj (hz : ‖z‖ = 1) : z⁻¹ = conj z := IsROrC.inv_eq_conj hz
+lemma inv_eq_conj (hz : ‖z‖ = 1) : z⁻¹ = conj z := RCLike.inv_eq_conj hz
 
 lemma exists_norm_eq_mul_self (z : ℂ) : ∃ c, ‖c‖ = 1 ∧ ‖z‖ = c * z :=
-  IsROrC.exists_norm_eq_mul_self _
+  RCLike.exists_norm_eq_mul_self _
 
 lemma exists_norm_mul_eq_self (z : ℂ) : ∃ c, ‖c‖ = 1 ∧ c * ‖z‖ = z :=
-  IsROrC.exists_norm_mul_eq_self _
+  RCLike.exists_norm_mul_eq_self _
 
-/-- The natural isomorphism between `𝕜` satisfying `IsROrC 𝕜` and `ℂ` when
-`IsROrC.im IsROrC.I = 1`. -/
+/-- The natural isomorphism between `𝕜` satisfying `RCLike 𝕜` and `ℂ` when
+`RCLike.im RCLike.I = 1`. -/
 @[simps]
-def _root_.IsROrC.complexRingEquiv {𝕜 : Type*} [IsROrC 𝕜] (h : IsROrC.im (IsROrC.I : 𝕜) = 1) :
-    𝕜 ≃+* ℂ where
-  toFun x := IsROrC.re x + IsROrC.im x * I
-  invFun x := re x + im x * IsROrC.I
+def _root_.RCLike.complexRingEquiv {𝕜 : Type*} [RCLike 𝕜]
+    (h : RCLike.im (RCLike.I : 𝕜) = 1) : 𝕜 ≃+* ℂ where
+  toFun x := RCLike.re x + RCLike.im x * I
+  invFun x := re x + im x * RCLike.I
   left_inv x := by simp
   right_inv x := by simp [h]
   map_add' x y := by simp only [map_add, ofReal_add]; ring
   map_mul' x y := by
-    simp only [IsROrC.mul_re, ofReal_sub, ofReal_mul, IsROrC.mul_im, ofReal_add]
+    simp only [RCLike.mul_re, ofReal_sub, ofReal_mul, RCLike.mul_im, ofReal_add]
     ring_nf
     rw [I_sq]
     ring
 
-/-- The natural `ℝ`-linear isometry equivalence between `𝕜` satisfying `IsROrC 𝕜` and `ℂ` when
-`IsROrC.im IsROrC.I = 1`. -/
+/-- The natural `ℝ`-linear isometry equivalence between `𝕜` satisfying `RCLike 𝕜` and `ℂ` when
+`RCLike.im RCLike.I = 1`. -/
 @[simps]
-def _root_.IsROrC.complexLinearIsometryEquiv {𝕜 : Type*} [IsROrC 𝕜]
-    (h : IsROrC.im (IsROrC.I : 𝕜) = 1) : 𝕜 ≃ₗᵢ[ℝ] ℂ where
-  map_smul' _ _ := by simp [IsROrC.smul_re, IsROrC.smul_im, ofReal_mul]; ring
+def _root_.RCLike.complexLinearIsometryEquiv {𝕜 : Type*} [RCLike 𝕜]
+    (h : RCLike.im (RCLike.I : 𝕜) = 1) : 𝕜 ≃ₗᵢ[ℝ] ℂ where
+  map_smul' _ _ := by simp [RCLike.smul_re, RCLike.smul_im, ofReal_mul]; ring
   norm_map' _ := by
-    rw [← sq_eq_sq (by positivity) (by positivity), ← normSq_eq_norm_sq, ← IsROrC.normSq_eq_def',
-      IsROrC.normSq_apply]
+    rw [← sq_eq_sq (by positivity) (by positivity), ← normSq_eq_norm_sq, ← RCLike.normSq_eq_def',
+      RCLike.normSq_apply]
     simp [normSq_add]
-  __ := IsROrC.complexRingEquiv h
+  __ := RCLike.complexRingEquiv h
 
 section ComplexOrder
 
@@ -516,73 +516,73 @@ end ComplexOrder
 
 end Complex
 
-namespace IsROrC
+namespace RCLike
 
 open ComplexConjugate
 
-local notation "reC" => @IsROrC.re ℂ _
-local notation "imC" => @IsROrC.im ℂ _
-local notation "IC" => @IsROrC.I ℂ _
-local notation "norm_sqC" => @IsROrC.normSq ℂ _
+local notation "reC" => @RCLike.re ℂ _
+local notation "imC" => @RCLike.im ℂ _
+local notation "IC" => @RCLike.I ℂ _
+local notation "norm_sqC" => @RCLike.normSq ℂ _
 
 @[simp]
 theorem re_to_complex {x : ℂ} : reC x = x.re :=
   rfl
-#align is_R_or_C.re_to_complex IsROrC.re_to_complex
+#align is_R_or_C.re_to_complex RCLike.re_to_complex
 
 @[simp]
 theorem im_to_complex {x : ℂ} : imC x = x.im :=
   rfl
-#align is_R_or_C.im_to_complex IsROrC.im_to_complex
+#align is_R_or_C.im_to_complex RCLike.im_to_complex
 
 @[simp]
 theorem I_to_complex : IC = Complex.I :=
   rfl
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.I_to_complex IsROrC.I_to_complex
+#align is_R_or_C.I_to_complex RCLike.I_to_complex
 
 @[simp]
 theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x :=
   rfl
-#align is_R_or_C.norm_sq_to_complex IsROrC.normSq_to_complex
+#align is_R_or_C.norm_sq_to_complex RCLike.normSq_to_complex
 
 section tsum
 
-variable {α : Type*} (𝕜 : Type*) [IsROrC 𝕜]
+variable {α : Type*} (𝕜 : Type*) [RCLike 𝕜]
 
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
   conjCLE.hasSum
-#align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
+#align is_R_or_C.has_sum_conj RCLike.hasSum_conj
 
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
   conjCLE.hasSum'
-#align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
+#align is_R_or_C.has_sum_conj' RCLike.hasSum_conj'
 
 @[simp]
 theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Summable f :=
   summable_star_iff
-#align is_R_or_C.summable_conj IsROrC.summable_conj
+#align is_R_or_C.summable_conj RCLike.summable_conj
 
 variable {𝕜}
 
 theorem conj_tsum (f : α → 𝕜) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   tsum_star
-#align is_R_or_C.conj_tsum IsROrC.conj_tsum
+#align is_R_or_C.conj_tsum RCLike.conj_tsum
 
 variable (𝕜)
 
 @[simp, norm_cast]
 theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : 𝕜)) x ↔ HasSum f x :=
-  ⟨fun h => by simpa only [IsROrC.reCLM_apply, IsROrC.ofReal_re] using reCLM.hasSum h,
+  ⟨fun h => by simpa only [RCLike.reCLM_apply, RCLike.ofReal_re] using reCLM.hasSum h,
     ofRealCLM.hasSum⟩
-#align is_R_or_C.has_sum_of_real IsROrC.hasSum_ofReal
+#align is_R_or_C.has_sum_of_real RCLike.hasSum_ofReal
 
 @[simp, norm_cast]
 theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : 𝕜)) ↔ Summable f :=
-  ⟨fun h => by simpa only [IsROrC.reCLM_apply, IsROrC.ofReal_re] using reCLM.summable h,
+  ⟨fun h => by simpa only [RCLike.reCLM_apply, RCLike.ofReal_re] using reCLM.summable h,
     ofRealCLM.summable⟩
-#align is_R_or_C.summable_of_real IsROrC.summable_ofReal
+#align is_R_or_C.summable_of_real RCLike.summable_ofReal
 
 @[norm_cast]
 theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, (f a : 𝕜) := by
@@ -590,23 +590,23 @@ theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, (f a
   · exact ContinuousLinearMap.map_tsum ofRealCLM h
   · rw [tsum_eq_zero_of_not_summable h,
       tsum_eq_zero_of_not_summable ((summable_ofReal _).not.mpr h), ofReal_zero]
-#align is_R_or_C.of_real_tsum IsROrC.ofReal_tsum
+#align is_R_or_C.of_real_tsum RCLike.ofReal_tsum
 
 theorem hasSum_re {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => re (f x)) (re x) :=
   reCLM.hasSum h
-#align is_R_or_C.has_sum_re IsROrC.hasSum_re
+#align is_R_or_C.has_sum_re RCLike.hasSum_re
 
 theorem hasSum_im {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => im (f x)) (im x) :=
   imCLM.hasSum h
-#align is_R_or_C.has_sum_im IsROrC.hasSum_im
+#align is_R_or_C.has_sum_im RCLike.hasSum_im
 
 theorem re_tsum {f : α → 𝕜} (h : Summable f) : re (∑' a, f a) = ∑' a, re (f a) :=
   reCLM.map_tsum h
-#align is_R_or_C.re_tsum IsROrC.re_tsum
+#align is_R_or_C.re_tsum RCLike.re_tsum
 
 theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a, im (f a) :=
   imCLM.map_tsum h
-#align is_R_or_C.im_tsum IsROrC.im_tsum
+#align is_R_or_C.im_tsum RCLike.im_tsum
 
 variable {𝕜}
 
@@ -616,16 +616,16 @@ theorem hasSum_iff (f : α → 𝕜) (c : 𝕜) :
   rintro ⟨h₁, h₂⟩
   simpa only [re_add_im] using
     ((hasSum_ofReal 𝕜).mpr h₁).add (((hasSum_ofReal 𝕜).mpr h₂).mul_right I)
-#align is_R_or_C.has_sum_iff IsROrC.hasSum_iff
+#align is_R_or_C.has_sum_iff RCLike.hasSum_iff
 
 end tsum
 
-end IsROrC
+end RCLike
 
 namespace Complex
 
 /-!
-We have to repeat the lemmas about `IsROrC.re` and `IsROrC.im` as they are not syntactic
+We have to repeat the lemmas about `RCLike.re` and `RCLike.im` as they are not syntactic
 matches for `Complex.re` and `Complex.im`.
 
 We do not have this problem with `ofReal` and `conj`, although we repeat them anyway for
@@ -639,58 +639,58 @@ variable {α : Type*}
 
 open ComplexConjugate
 
--- Porting note: @[simp] unneeded due to `IsROrC.hasSum_conj`
+-- Porting note: @[simp] unneeded due to `RCLike.hasSum_conj`
 theorem hasSum_conj {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
-  IsROrC.hasSum_conj _
+  RCLike.hasSum_conj _
 #align complex.has_sum_conj Complex.hasSum_conj
 
 theorem hasSum_conj' {f : α → ℂ} {x : ℂ} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
-  IsROrC.hasSum_conj' _
+  RCLike.hasSum_conj' _
 #align complex.has_sum_conj' Complex.hasSum_conj'
 
--- Porting note: @[simp] unneeded due to `IsROrC.summable_conj`
+-- Porting note: @[simp] unneeded due to `RCLike.summable_conj`
 theorem summable_conj {f : α → ℂ} : (Summable fun x => conj (f x)) ↔ Summable f :=
-  IsROrC.summable_conj _
+  RCLike.summable_conj _
 #align complex.summable_conj Complex.summable_conj
 
 theorem conj_tsum (f : α → ℂ) : conj (∑' a, f a) = ∑' a, conj (f a) :=
-  IsROrC.conj_tsum _
+  RCLike.conj_tsum _
 #align complex.conj_tsum Complex.conj_tsum
 
 @[simp, norm_cast]
 theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : ℂ)) x ↔ HasSum f x :=
-  IsROrC.hasSum_ofReal _
+  RCLike.hasSum_ofReal _
 #align complex.has_sum_of_real Complex.hasSum_ofReal
 
 @[simp, norm_cast]
 theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : ℂ)) ↔ Summable f :=
-  IsROrC.summable_ofReal _
+  RCLike.summable_ofReal _
 #align complex.summable_of_real Complex.summable_ofReal
 
 @[norm_cast]
 theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : ℂ) = ∑' a, ↑(f a) :=
-  IsROrC.ofReal_tsum _ _
+  RCLike.ofReal_tsum _ _
 #align complex.of_real_tsum Complex.ofReal_tsum
 
 theorem hasSum_re {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).re) x.re :=
-  IsROrC.hasSum_re _ h
+  RCLike.hasSum_re _ h
 #align complex.has_sum_re Complex.hasSum_re
 
 theorem hasSum_im {f : α → ℂ} {x : ℂ} (h : HasSum f x) : HasSum (fun x => (f x).im) x.im :=
-  IsROrC.hasSum_im _ h
+  RCLike.hasSum_im _ h
 #align complex.has_sum_im Complex.hasSum_im
 
 theorem re_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).re = ∑' a, (f a).re :=
-  IsROrC.re_tsum _ h
+  RCLike.re_tsum _ h
 #align complex.re_tsum Complex.re_tsum
 
 theorem im_tsum {f : α → ℂ} (h : Summable f) : (∑' a, f a).im = ∑' a, (f a).im :=
-  IsROrC.im_tsum _ h
+  RCLike.im_tsum _ h
 #align complex.im_tsum Complex.im_tsum
 
 theorem hasSum_iff (f : α → ℂ) (c : ℂ) :
     HasSum f c ↔ HasSum (fun x => (f x).re) c.re ∧ HasSum (fun x => (f x).im) c.im :=
-  IsROrC.hasSum_iff _ _
+  RCLike.hasSum_iff _ _
 #align complex.has_sum_iff Complex.hasSum_iff
 
 end tsum

This adds a shortcut instance for T2Space ℂ in Analysis.Complex.Basic.

See this thread on Zulip.

@@ -238,6 +238,8 @@ theorem uniformEmbedding_equivRealProd : UniformEmbedding equivRealProd :=
 instance : CompleteSpace ℂ :=
   (completeSpace_congr uniformEmbedding_equivRealProd).mpr inferInstance
 
+instance instT2Space : T2Space ℂ := TopologicalSpace.t2Space_of_metrizableSpace
+
 /-- The natural `ContinuousLinearEquiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps! (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
 def equivRealProdCLM : ℂ ≃L[ℝ] ℝ × ℝ :=

We show the Fourier inversion formula on finite-dimensional real inner product spaces: if f and its Fourier transform are both integrable, then 𝓕⁻ (𝓕 f) = f at continuity points of f.

@@ -400,6 +400,10 @@ theorem continuous_ofReal : Continuous ((↑) : ℝ → ℂ) :=
   ofRealLI.continuous
 #align complex.continuous_of_real Complex.continuous_ofReal
 
+lemma _root_.Filter.Tendsto.ofReal {α : Type*} {l : Filter α} {f : α → ℝ} {x : ℝ}
+    (hf : Tendsto f l (𝓝 x)) : Tendsto (fun x ↦ (f x : ℂ)) l (𝓝 (x : ℂ)) :=
+  (continuous_ofReal.tendsto _).comp hf
+
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
 theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) : f = Complex.ofReal := by
   convert congr_arg AlgHom.toRingHom <| Subsingleton.elim (AlgHom.mk' f <| map_real_smul f h)

This PR cleans up some lemmas where we're taking named instance parameters [h : Nat.AtLeastTwo n] and manually proving inequalities like 0 < n from h by adding an instance of NeZero n from Nat.AtLeastTwo n as well as a couple of other helper lemmas.

This removes Nat.AtLeastTwo.ne_zero, as NeZero.ne_zero replaces it.

@@ -724,8 +724,8 @@ lemma nat_cast_mem_slitPlane {n : ℕ} : ↑n ∈ slitPlane ↔ n ≠ 0 := by
   simpa [pos_iff_ne_zero] using @ofReal_mem_slitPlane n
 
 @[simp]
-lemma ofNat_mem_slitPlane (n : ℕ) [h : n.AtLeastTwo] : no_index (OfNat.ofNat n) ∈ slitPlane :=
-  nat_cast_mem_slitPlane.2 h.ne_zero
+lemma ofNat_mem_slitPlane (n : ℕ) [n.AtLeastTwo] : no_index (OfNat.ofNat n) ∈ slitPlane :=
+  nat_cast_mem_slitPlane.2 (NeZero.ne n)
 
 lemma mem_slitPlane_iff_not_le_zero {z : ℂ} : z ∈ slitPlane ↔ ¬z ≤ 0 :=
   mem_slitPlane_iff.trans not_le_zero_iff.symm

Co-authored-by: L Lllvvuu <git@llllvvuu.dev>

@@ -269,7 +269,7 @@ def reCLM : ℂ →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by simp [abs_re_le_abs]
 #align complex.re_clm Complex.reCLM
 
-@[continuity]
+@[continuity, fun_prop]
 theorem continuous_re : Continuous re :=
   reCLM.continuous
 #align complex.continuous_re Complex.continuous_re
@@ -289,7 +289,7 @@ def imCLM : ℂ →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by simp [abs_im_le_abs]
 #align complex.im_clm Complex.imCLM
 
-@[continuity]
+@[continuity, fun_prop]
 theorem continuous_im : Continuous im :=
   imCLM.continuous
 #align complex.continuous_im Complex.continuous_im
@@ -395,7 +395,7 @@ theorem isometry_ofReal : Isometry ((↑) : ℝ → ℂ) :=
   ofRealLI.isometry
 #align complex.isometry_of_real Complex.isometry_ofReal
 
-@[continuity]
+@[continuity, fun_prop]
 theorem continuous_ofReal : Continuous ((↑) : ℝ → ℂ) :=
   ofRealLI.continuous
 #align complex.continuous_of_real Complex.continuous_ofReal

A goal about real numbers should not suddenly turn into a goal about complex numbers!

@@ -171,7 +171,7 @@ theorem norm_nat (n : ℕ) : ‖(n : ℂ)‖ = n :=
 #align complex.norm_nat Complex.norm_nat
 
 @[simp 1100]
-theorem norm_int {n : ℤ} : ‖(n : ℂ)‖ = |(n : ℝ)| := (int_cast_abs n).symm
+lemma norm_int {n : ℤ} : ‖(n : ℂ)‖ = |(n : ℝ)| := abs_intCast n
 #align complex.norm_int Complex.norm_int
 
 theorem norm_int_of_nonneg {n : ℤ} (hn : 0 ≤ n) : ‖(n : ℂ)‖ = n := by

This adds some instances regarding normed algebra structures to RestrictScalars to mimic those for normed spaces.

In addition, given a normed ℂ-algebra, this puts a normed ℝ-algebra structure on the same space. This is not adding any new data instances, as these already exist from Algebra.complexToReal.

@@ -81,7 +81,7 @@ instance {R : Type*} [NormedField R] [NormedAlgebra R ℝ] : NormedAlgebra R ℂ
     rw [← algebraMap_smul ℝ r x, real_smul, norm_mul, norm_eq_abs, abs_ofReal, ← Real.norm_eq_abs,
       norm_algebraMap']
 
-variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E]
+variable {E : Type*} [SeminormedAddCommGroup E] [NormedSpace ℂ E]
 
 -- see Note [lower instance priority]
 /-- The module structure from `Module.complexToReal` is a normed space. -/
@@ -89,6 +89,12 @@ instance (priority := 900) _root_.NormedSpace.complexToReal : NormedSpace ℝ E
   NormedSpace.restrictScalars ℝ ℂ E
 #align normed_space.complex_to_real NormedSpace.complexToReal
 
+-- see Note [lower instance priority]
+/-- The algebra structure from `Algebra.complexToReal` is a normed algebra. -/
+instance (priority := 900) _root_.NormedAlgebra.complexToReal {A : Type*} [SeminormedRing A]
+    [NormedAlgebra ℂ A] : NormedAlgebra ℝ A :=
+  NormedAlgebra.restrictScalars ℝ ℂ A
+
 theorem dist_eq (z w : ℂ) : dist z w = abs (z - w) :=
   rfl
 #align complex.dist_eq Complex.dist_eq

@@ -694,9 +694,9 @@ open scoped ComplexOrder
 /-- The *slit plane* is the complex plane with the closed negative real axis removed. -/
 def slitPlane : Set ℂ := {z | 0 < z.re ∨ z.im ≠ 0}
 
-lemma mem_slitPlane_iff {z : ℂ} : z ∈ slitPlane ↔ 0 < z.re ∨ z.im ≠ 0 := Iff.rfl
+lemma mem_slitPlane_iff {z : ℂ} : z ∈ slitPlane ↔ 0 < z.re ∨ z.im ≠ 0 := Set.mem_setOf
 
-lemma slitPlane_eq_union : slitPlane = {z | 0 < z.re} ∪ {z | z.im ≠ 0} := rfl
+lemma slitPlane_eq_union : slitPlane = {z | 0 < z.re} ∪ {z | z.im ≠ 0} := Set.setOf_or.symm
 
 lemma isOpen_slitPlane : IsOpen slitPlane :=
   (isOpen_lt continuous_const continuous_re).union (isOpen_ne_fun continuous_im continuous_const)

This adds an OrderClosedTopology instance (scoped to ComplexOrder) for the complex numbers (to make things like tsum_le_tsum work with the partial order on the complex numbers) and the fact that Complex.ofReal' is monotone with respect to this order.

Co-authored-by: Michael Stoll <99838730+MichaelStollBayreuth@users.noreply.github.com>

@@ -491,6 +491,15 @@ theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
   rw [norm_eq_abs, abs_ofReal, _root_.abs_of_nonneg (id hz.1 : 0 ≤ z)]
 #align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg
 
+/-- We show that the partial order and the topology on `ℂ` are compatible.
+We turn this into an instance scoped to `ComplexOrder`. -/
+lemma orderClosedTopology : OrderClosedTopology ℂ where
+  isClosed_le' := by
+    simp_rw [le_def, Set.setOf_and]
+    refine IsClosed.inter (isClosed_le ?_ ?_) (isClosed_eq ?_ ?_) <;> continuity
+
+scoped[ComplexOrder] attribute [instance] Complex.orderClosedTopology
+
 end ComplexOrder
 
 end Complex

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

From LeanAPAP

@@ -105,7 +105,7 @@ theorem dist_mk (x₁ y₁ x₂ y₂ : ℝ) :
 #align complex.dist_mk Complex.dist_mk
 
 theorem dist_of_re_eq {z w : ℂ} (h : z.re = w.re) : dist z w = dist z.im w.im := by
-  rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, zero_add, Real.sqrt_sq_eq_abs, Real.dist_eq]
+  rw [dist_eq_re_im, h, sub_self, zero_pow two_ne_zero, zero_add, Real.sqrt_sq_eq_abs, Real.dist_eq]
 #align complex.dist_of_re_eq Complex.dist_of_re_eq
 
 theorem nndist_of_re_eq {z w : ℂ} (h : z.re = w.re) : nndist z w = nndist z.im w.im :=
@@ -117,7 +117,7 @@ theorem edist_of_re_eq {z w : ℂ} (h : z.re = w.re) : edist z w = edist z.im w.
 #align complex.edist_of_re_eq Complex.edist_of_re_eq
 
 theorem dist_of_im_eq {z w : ℂ} (h : z.im = w.im) : dist z w = dist z.re w.re := by
-  rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, add_zero, Real.sqrt_sq_eq_abs, Real.dist_eq]
+  rw [dist_eq_re_im, h, sub_self, zero_pow two_ne_zero, add_zero, Real.sqrt_sq_eq_abs, Real.dist_eq]
 #align complex.dist_of_im_eq Complex.dist_of_im_eq
 
 theorem nndist_of_im_eq {z w : ℂ} (h : z.im = w.im) : nndist z w = nndist z.re w.re :=

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.

@@ -23,14 +23,14 @@ This file registers `ℂ` as a normed field, expresses basic properties of the n
 tools on the real vector space structure of `ℂ`. Notably, in the namespace `Complex`,
 it defines functions:
 
-* `reClm`
-* `imClm`
-* `ofRealClm`
-* `conjCle`
+* `reCLM`
+* `imCLM`
+* `ofRealCLM`
+* `conjCLE`
 
 They are bundled versions of the real part, the imaginary part, the embedding of `ℝ` in `ℂ`, and
 the complex conjugate as continuous `ℝ`-linear maps. The last two are also bundled as linear
-isometries in `ofRealLi` and `conjLie`.
+isometries in `ofRealLI` and `conjLIE`.
 
 We also register the fact that `ℂ` is an `IsROrC` field.
 -/
@@ -234,16 +234,16 @@ instance : CompleteSpace ℂ :=
 
 /-- The natural `ContinuousLinearEquiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps! (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
-def equivRealProdClm : ℂ ≃L[ℝ] ℝ × ℝ :=
+def equivRealProdCLM : ℂ ≃L[ℝ] ℝ × ℝ :=
   equivRealProdLm.toContinuousLinearEquivOfBounds 1 (Real.sqrt 2) equivRealProd_apply_le' fun p =>
     abs_le_sqrt_two_mul_max (equivRealProd.symm p)
-#align complex.equiv_real_prod_clm Complex.equivRealProdClm
+#align complex.equiv_real_prod_clm Complex.equivRealProdCLM
 
-theorem equivRealProdClm_symm_apply (p : ℝ × ℝ) :
-    Complex.equivRealProdClm.symm p = p.1 + p.2 * Complex.I := Complex.equivRealProd_symm_apply p
+theorem equivRealProdCLM_symm_apply (p : ℝ × ℝ) :
+    Complex.equivRealProdCLM.symm p = p.1 + p.2 * Complex.I := Complex.equivRealProd_symm_apply p
 
 instance : ProperSpace ℂ :=
-  (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdClm.toHomeomorph).properSpace
+  (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdCLM.toHomeomorph).properSpace
 
 /-- The `abs` function on `ℂ` is proper. -/
 theorem tendsto_abs_cocompact_atTop : Tendsto abs (cocompact ℂ) atTop :=
@@ -259,48 +259,48 @@ theorem tendsto_normSq_cocompact_atTop : Tendsto normSq (cocompact ℂ) atTop :=
 open ContinuousLinearMap
 
 /-- Continuous linear map version of the real part function, from `ℂ` to `ℝ`. -/
-def reClm : ℂ →L[ℝ] ℝ :=
+def reCLM : ℂ →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by simp [abs_re_le_abs]
-#align complex.re_clm Complex.reClm
+#align complex.re_clm Complex.reCLM
 
 @[continuity]
 theorem continuous_re : Continuous re :=
-  reClm.continuous
+  reCLM.continuous
 #align complex.continuous_re Complex.continuous_re
 
 @[simp]
-theorem reClm_coe : (reClm : ℂ →ₗ[ℝ] ℝ) = reLm :=
+theorem reCLM_coe : (reCLM : ℂ →ₗ[ℝ] ℝ) = reLm :=
   rfl
-#align complex.re_clm_coe Complex.reClm_coe
+#align complex.re_clm_coe Complex.reCLM_coe
 
 @[simp]
-theorem reClm_apply (z : ℂ) : (reClm : ℂ → ℝ) z = z.re :=
+theorem reCLM_apply (z : ℂ) : (reCLM : ℂ → ℝ) z = z.re :=
   rfl
-#align complex.re_clm_apply Complex.reClm_apply
+#align complex.re_clm_apply Complex.reCLM_apply
 
 /-- Continuous linear map version of the imaginary part function, from `ℂ` to `ℝ`. -/
-def imClm : ℂ →L[ℝ] ℝ :=
+def imCLM : ℂ →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by simp [abs_im_le_abs]
-#align complex.im_clm Complex.imClm
+#align complex.im_clm Complex.imCLM
 
 @[continuity]
 theorem continuous_im : Continuous im :=
-  imClm.continuous
+  imCLM.continuous
 #align complex.continuous_im Complex.continuous_im
 
 @[simp]
-theorem imClm_coe : (imClm : ℂ →ₗ[ℝ] ℝ) = imLm :=
+theorem imCLM_coe : (imCLM : ℂ →ₗ[ℝ] ℝ) = imLm :=
   rfl
-#align complex.im_clm_coe Complex.imClm_coe
+#align complex.im_clm_coe Complex.imCLM_coe
 
 @[simp]
-theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
+theorem imCLM_apply (z : ℂ) : (imCLM : ℂ → ℝ) z = z.im :=
   rfl
-#align complex.im_clm_apply Complex.imClm_apply
+#align complex.im_clm_apply Complex.imCLM_apply
 
 theorem restrictScalars_one_smulRight' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smulRight x : ℂ →L[ℂ] E) =
-      reClm.smulRight x + I • imClm.smulRight x := by
+      reCLM.smulRight x + I • imCLM.smulRight x := by
   ext ⟨a, b⟩
   simp [mk_eq_add_mul_I, mul_smul, smul_comm I b x]
 #align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'
@@ -314,22 +314,22 @@ theorem restrictScalars_one_smulRight (x : ℂ) :
 #align complex.restrict_scalars_one_smul_right Complex.restrictScalars_one_smulRight
 
 /-- The complex-conjugation function from `ℂ` to itself is an isometric linear equivalence. -/
-def conjLie : ℂ ≃ₗᵢ[ℝ] ℂ :=
+def conjLIE : ℂ ≃ₗᵢ[ℝ] ℂ :=
   ⟨conjAe.toLinearEquiv, abs_conj⟩
-#align complex.conj_lie Complex.conjLie
+#align complex.conj_lie Complex.conjLIE
 
 @[simp]
-theorem conjLie_apply (z : ℂ) : conjLie z = conj z :=
+theorem conjLIE_apply (z : ℂ) : conjLIE z = conj z :=
   rfl
-#align complex.conj_lie_apply Complex.conjLie_apply
+#align complex.conj_lie_apply Complex.conjLIE_apply
 
 @[simp]
-theorem conjLie_symm : conjLie.symm = conjLie :=
+theorem conjLIE_symm : conjLIE.symm = conjLIE :=
   rfl
-#align complex.conj_lie_symm Complex.conjLie_symm
+#align complex.conj_lie_symm Complex.conjLIE_symm
 
 theorem isometry_conj : Isometry (conj : ℂ → ℂ) :=
-  conjLie.isometry
+  conjLIE.isometry
 #align complex.isometry_conj Complex.isometry_conj
 
 @[simp]
@@ -351,7 +351,7 @@ theorem nndist_conj_comm (z w : ℂ) : nndist (conj z) w = nndist z (conj w) :=
 #align complex.nndist_conj_comm Complex.nndist_conj_comm
 
 instance : ContinuousStar ℂ :=
-  ⟨conjLie.continuous⟩
+  ⟨conjLIE.continuous⟩
 
 @[continuity]
 theorem continuous_conj : Continuous (conj : ℂ → ℂ) :=
@@ -366,32 +366,32 @@ theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous
 #align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuous
 
 /-- Continuous linear equiv version of the conj function, from `ℂ` to `ℂ`. -/
-def conjCle : ℂ ≃L[ℝ] ℂ :=
-  conjLie
-#align complex.conj_cle Complex.conjCle
+def conjCLE : ℂ ≃L[ℝ] ℂ :=
+  conjLIE
+#align complex.conj_cle Complex.conjCLE
 
 @[simp]
-theorem conjCle_coe : conjCle.toLinearEquiv = conjAe.toLinearEquiv :=
+theorem conjCLE_coe : conjCLE.toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
-#align complex.conj_cle_coe Complex.conjCle_coe
+#align complex.conj_cle_coe Complex.conjCLE_coe
 
 @[simp]
-theorem conjCle_apply (z : ℂ) : conjCle z = conj z :=
+theorem conjCLE_apply (z : ℂ) : conjCLE z = conj z :=
   rfl
-#align complex.conj_cle_apply Complex.conjCle_apply
+#align complex.conj_cle_apply Complex.conjCLE_apply
 
 /-- Linear isometry version of the canonical embedding of `ℝ` in `ℂ`. -/
-def ofRealLi : ℝ →ₗᵢ[ℝ] ℂ :=
+def ofRealLI : ℝ →ₗᵢ[ℝ] ℂ :=
   ⟨ofRealAm.toLinearMap, norm_real⟩
-#align complex.of_real_li Complex.ofRealLi
+#align complex.of_real_li Complex.ofRealLI
 
 theorem isometry_ofReal : Isometry ((↑) : ℝ → ℂ) :=
-  ofRealLi.isometry
+  ofRealLI.isometry
 #align complex.isometry_of_real Complex.isometry_ofReal
 
 @[continuity]
 theorem continuous_ofReal : Continuous ((↑) : ℝ → ℂ) :=
-  ofRealLi.continuous
+  ofRealLI.continuous
 #align complex.continuous_of_real Complex.continuous_ofReal
 
 /-- The only continuous ring homomorphism from `ℝ` to `ℂ` is the identity. -/
@@ -401,19 +401,19 @@ theorem ringHom_eq_ofReal_of_continuous {f : ℝ →+* ℂ} (h : Continuous f) :
 #align complex.ring_hom_eq_of_real_of_continuous Complex.ringHom_eq_ofReal_of_continuous
 
 /-- Continuous linear map version of the canonical embedding of `ℝ` in `ℂ`. -/
-def ofRealClm : ℝ →L[ℝ] ℂ :=
-  ofRealLi.toContinuousLinearMap
-#align complex.of_real_clm Complex.ofRealClm
+def ofRealCLM : ℝ →L[ℝ] ℂ :=
+  ofRealLI.toContinuousLinearMap
+#align complex.of_real_clm Complex.ofRealCLM
 
 @[simp]
-theorem ofRealClm_coe : (ofRealClm : ℝ →ₗ[ℝ] ℂ) = ofRealAm.toLinearMap :=
+theorem ofRealCLM_coe : (ofRealCLM : ℝ →ₗ[ℝ] ℂ) = ofRealAm.toLinearMap :=
   rfl
-#align complex.of_real_clm_coe Complex.ofRealClm_coe
+#align complex.of_real_clm_coe Complex.ofRealCLM_coe
 
 @[simp]
-theorem ofRealClm_apply (x : ℝ) : ofRealClm x = x :=
+theorem ofRealCLM_apply (x : ℝ) : ofRealCLM x = x :=
   rfl
-#align complex.of_real_clm_apply Complex.ofRealClm_apply
+#align complex.of_real_clm_apply Complex.ofRealCLM_apply
 
 noncomputable instance : IsROrC ℂ where
   re := ⟨⟨Complex.re, Complex.zero_re⟩, Complex.add_re⟩
@@ -531,11 +531,11 @@ variable {α : Type*} (𝕜 : Type*) [IsROrC 𝕜]
 
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
-  conjCle.hasSum
+  conjCLE.hasSum
 #align is_R_or_C.has_sum_conj IsROrC.hasSum_conj
 
 theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) (conj x) ↔ HasSum f x :=
-  conjCle.hasSum'
+  conjCLE.hasSum'
 #align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
 
 @[simp]
@@ -553,38 +553,38 @@ variable (𝕜)
 
 @[simp, norm_cast]
 theorem hasSum_ofReal {f : α → ℝ} {x : ℝ} : HasSum (fun x => (f x : 𝕜)) x ↔ HasSum f x :=
-  ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using reClm.hasSum h,
-    ofRealClm.hasSum⟩
+  ⟨fun h => by simpa only [IsROrC.reCLM_apply, IsROrC.ofReal_re] using reCLM.hasSum h,
+    ofRealCLM.hasSum⟩
 #align is_R_or_C.has_sum_of_real IsROrC.hasSum_ofReal
 
 @[simp, norm_cast]
 theorem summable_ofReal {f : α → ℝ} : (Summable fun x => (f x : 𝕜)) ↔ Summable f :=
-  ⟨fun h => by simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using reClm.summable h,
-    ofRealClm.summable⟩
+  ⟨fun h => by simpa only [IsROrC.reCLM_apply, IsROrC.ofReal_re] using reCLM.summable h,
+    ofRealCLM.summable⟩
 #align is_R_or_C.summable_of_real IsROrC.summable_ofReal
 
 @[norm_cast]
 theorem ofReal_tsum (f : α → ℝ) : (↑(∑' a, f a) : 𝕜) = ∑' a, (f a : 𝕜) := by
   by_cases h : Summable f
-  · exact ContinuousLinearMap.map_tsum ofRealClm h
+  · exact ContinuousLinearMap.map_tsum ofRealCLM h
   · rw [tsum_eq_zero_of_not_summable h,
       tsum_eq_zero_of_not_summable ((summable_ofReal _).not.mpr h), ofReal_zero]
 #align is_R_or_C.of_real_tsum IsROrC.ofReal_tsum
 
 theorem hasSum_re {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => re (f x)) (re x) :=
-  reClm.hasSum h
+  reCLM.hasSum h
 #align is_R_or_C.has_sum_re IsROrC.hasSum_re
 
 theorem hasSum_im {f : α → 𝕜} {x : 𝕜} (h : HasSum f x) : HasSum (fun x => im (f x)) (im x) :=
-  imClm.hasSum h
+  imCLM.hasSum h
 #align is_R_or_C.has_sum_im IsROrC.hasSum_im
 
 theorem re_tsum {f : α → 𝕜} (h : Summable f) : re (∑' a, f a) = ∑' a, re (f a) :=
-  reClm.map_tsum h
+  reCLM.map_tsum h
 #align is_R_or_C.re_tsum IsROrC.re_tsum
 
 theorem im_tsum {f : α → 𝕜} (h : Summable f) : im (∑' a, f a) = ∑' a, im (f a) :=
-  imClm.map_tsum h
+  imCLM.map_tsum h
 #align is_R_or_C.im_tsum IsROrC.im_tsum
 
 variable {𝕜}

This adds ring isomorphisms and linear isometry equivalences between 𝕜 satisfying IsROrC 𝕜 and ℝ or ℂ depending on whether I = 0 or im I = 1. Of course, the design of IsROrC is meant to eliminate the need for such things most of the time, but these are helpful in the rare case one actually does need to split into the two cases in the middle of a proof.

@@ -172,6 +172,9 @@ theorem norm_int_of_nonneg {n : ℤ} (hn : 0 ≤ n) : ‖(n : ℂ)‖ = n := by
   rw [norm_int, ← Int.cast_abs, _root_.abs_of_nonneg hn]
 #align complex.norm_int_of_nonneg Complex.norm_int_of_nonneg
 
+lemma normSq_eq_norm_sq (z : ℂ) : normSq z = ‖z‖ ^ 2 := by
+  rw [normSq_eq_abs, norm_eq_abs]
+
 @[continuity]
 theorem continuous_abs : Continuous abs :=
   continuous_norm
@@ -451,6 +454,34 @@ lemma exists_norm_eq_mul_self (z : ℂ) : ∃ c, ‖c‖ = 1 ∧ ‖z‖ = c * z
 lemma exists_norm_mul_eq_self (z : ℂ) : ∃ c, ‖c‖ = 1 ∧ c * ‖z‖ = z :=
   IsROrC.exists_norm_mul_eq_self _
 
+/-- The natural isomorphism between `𝕜` satisfying `IsROrC 𝕜` and `ℂ` when
+`IsROrC.im IsROrC.I = 1`. -/
+@[simps]
+def _root_.IsROrC.complexRingEquiv {𝕜 : Type*} [IsROrC 𝕜] (h : IsROrC.im (IsROrC.I : 𝕜) = 1) :
+    𝕜 ≃+* ℂ where
+  toFun x := IsROrC.re x + IsROrC.im x * I
+  invFun x := re x + im x * IsROrC.I
+  left_inv x := by simp
+  right_inv x := by simp [h]
+  map_add' x y := by simp only [map_add, ofReal_add]; ring
+  map_mul' x y := by
+    simp only [IsROrC.mul_re, ofReal_sub, ofReal_mul, IsROrC.mul_im, ofReal_add]
+    ring_nf
+    rw [I_sq]
+    ring
+
+/-- The natural `ℝ`-linear isometry equivalence between `𝕜` satisfying `IsROrC 𝕜` and `ℂ` when
+`IsROrC.im IsROrC.I = 1`. -/
+@[simps]
+def _root_.IsROrC.complexLinearIsometryEquiv {𝕜 : Type*} [IsROrC 𝕜]
+    (h : IsROrC.im (IsROrC.I : 𝕜) = 1) : 𝕜 ≃ₗᵢ[ℝ] ℂ where
+  map_smul' _ _ := by simp [IsROrC.smul_re, IsROrC.smul_im, ofReal_mul]; ring
+  norm_map' _ := by
+    rw [← sq_eq_sq (by positivity) (by positivity), ← normSq_eq_norm_sq, ← IsROrC.normSq_eq_def',
+      IsROrC.normSq_apply]
+    simp [normSq_add]
+  __ := IsROrC.complexRingEquiv h
+
 section ComplexOrder
 
 open ComplexOrder

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -359,7 +359,7 @@ theorem continuous_conj : Continuous (conj : ℂ → ℂ) :=
 conjugation. -/
 theorem ringHom_eq_id_or_conj_of_continuous {f : ℂ →+* ℂ} (hf : Continuous f) :
     f = RingHom.id ℂ ∨ f = conj := by
-  simpa only [FunLike.ext_iff] using real_algHom_eq_id_or_conj (AlgHom.mk' f (map_real_smul f hf))
+  simpa only [DFunLike.ext_iff] using real_algHom_eq_id_or_conj (AlgHom.mk' f (map_real_smul f hf))
 #align complex.ring_hom_eq_id_or_conj_of_continuous Complex.ringHom_eq_id_or_conj_of_continuous
 
 /-- Continuous linear equiv version of the conj function, from `ℂ` to `ℂ`. -/

and other simple lemmas

From LeanAPAP

@@ -41,6 +41,7 @@ assert_not_exists Absorbs
 noncomputable section
 
 namespace Complex
+variable {z : ℂ}
 
 open ComplexConjugate Topology Filter
 
@@ -52,6 +53,8 @@ theorem norm_eq_abs (z : ℂ) : ‖z‖ = abs z :=
   rfl
 #align complex.norm_eq_abs Complex.norm_eq_abs
 
+lemma norm_I : ‖I‖ = 1 := abs_I
+
 theorem norm_exp_ofReal_mul_I (t : ℝ) : ‖exp (t * I)‖ = 1 := by
   simp only [norm_eq_abs, abs_exp_ofReal_mul_I]
 set_option linter.uppercaseLean3 false in
@@ -436,6 +439,18 @@ theorem _root_.IsROrC.im_eq_complex_im : ⇑(IsROrC.im : ℂ →+ ℝ) = Complex
   rfl
 #align is_R_or_C.im_eq_complex_im IsROrC.im_eq_complex_im
 
+-- TODO: Replace `mul_conj` and `conj_mul` once `norm` has replaced `abs`
+lemma mul_conj' (z : ℂ) : z * conj z = ‖z‖ ^ 2 := IsROrC.mul_conj z
+lemma conj_mul' (z : ℂ) : conj z * z = ‖z‖ ^ 2 := IsROrC.conj_mul z
+
+lemma inv_eq_conj (hz : ‖z‖ = 1) : z⁻¹ = conj z := IsROrC.inv_eq_conj hz
+
+lemma exists_norm_eq_mul_self (z : ℂ) : ∃ c, ‖c‖ = 1 ∧ ‖z‖ = c * z :=
+  IsROrC.exists_norm_eq_mul_self _
+
+lemma exists_norm_mul_eq_self (z : ℂ) : ∃ c, ‖c‖ = 1 ∧ c * ‖z‖ = z :=
+  IsROrC.exists_norm_mul_eq_self _
+
 section ComplexOrder
 
 open ComplexOrder

See Zulip thread for the discussion.

@@ -195,7 +195,7 @@ theorem nnnorm_int (n : ℤ) : ‖(n : ℂ)‖₊ = ‖n‖₊ :=
 #align complex.nnnorm_int Complex.nnnorm_int
 
 theorem nnnorm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖₊ = 1 :=
-  (pow_left_inj zero_le' zero_le' hn).1 $ by rw [← nnnorm_pow, h, nnnorm_one, one_pow]
+  (pow_left_inj zero_le' zero_le' hn).1 <| by rw [← nnnorm_pow, h, nnnorm_one, one_pow]
 #align complex.nnnorm_eq_one_of_pow_eq_one Complex.nnnorm_eq_one_of_pow_eq_one
 
 theorem norm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖ = 1 :=

In preparation of future PRs dealing with estimates of the complex logarithm and its Taylor series, this introduces Complex.slitPlane for the set of complex numbers not on the closed negative real axis (in Analysis.SpecialFunctions.Complex.Arg), adds a bunch of API lemmas, and replaces hypotheses of the form 0 < x.re ∨ x.im ≠ 0 by x ∈ slitPlane in several other files.

(We do not introduce a new file for that to avoid circular imports with Analysis.SpecialFunctions.Complex.Arg.)

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -628,4 +628,62 @@ theorem hasSum_iff (f : α → ℂ) (c : ℂ) :
 
 end tsum
 
+section slitPlane
+
+/-!
+### Define the "slit plane" `ℂ ∖ ℝ≤0` and provide some API
+-/
+
+open scoped ComplexOrder
+
+/-- The *slit plane* is the complex plane with the closed negative real axis removed. -/
+def slitPlane : Set ℂ := {z | 0 < z.re ∨ z.im ≠ 0}
+
+lemma mem_slitPlane_iff {z : ℂ} : z ∈ slitPlane ↔ 0 < z.re ∨ z.im ≠ 0 := Iff.rfl
+
+lemma slitPlane_eq_union : slitPlane = {z | 0 < z.re} ∪ {z | z.im ≠ 0} := rfl
+
+lemma isOpen_slitPlane : IsOpen slitPlane :=
+  (isOpen_lt continuous_const continuous_re).union (isOpen_ne_fun continuous_im continuous_const)
+
+@[simp]
+lemma ofReal_mem_slitPlane {x : ℝ} : ↑x ∈ slitPlane ↔ 0 < x := by simp [mem_slitPlane_iff]
+
+@[simp]
+lemma neg_ofReal_mem_slitPlane {x : ℝ} : -↑x ∈ slitPlane ↔ x < 0 := by
+  simpa using ofReal_mem_slitPlane (x := -x)
+
+@[simp] lemma one_mem_slitPlane : 1 ∈ slitPlane := ofReal_mem_slitPlane.2 one_pos
+
+@[simp]
+lemma zero_not_mem_slitPlane : 0 ∉ slitPlane := mt ofReal_mem_slitPlane.1 (lt_irrefl _)
+
+@[simp]
+lemma nat_cast_mem_slitPlane {n : ℕ} : ↑n ∈ slitPlane ↔ n ≠ 0 := by
+  simpa [pos_iff_ne_zero] using @ofReal_mem_slitPlane n
+
+@[simp]
+lemma ofNat_mem_slitPlane (n : ℕ) [h : n.AtLeastTwo] : no_index (OfNat.ofNat n) ∈ slitPlane :=
+  nat_cast_mem_slitPlane.2 h.ne_zero
+
+lemma mem_slitPlane_iff_not_le_zero {z : ℂ} : z ∈ slitPlane ↔ ¬z ≤ 0 :=
+  mem_slitPlane_iff.trans not_le_zero_iff.symm
+
+protected lemma compl_Iic_zero : (Set.Iic 0)ᶜ = slitPlane := Set.ext fun _ ↦
+  mem_slitPlane_iff_not_le_zero.symm
+
+lemma slitPlane_ne_zero {z : ℂ} (hz : z ∈ slitPlane) : z ≠ 0 :=
+  ne_of_mem_of_not_mem hz zero_not_mem_slitPlane
+
+/-- The slit plane includes the open unit ball of radius `1` around `1`. -/
+lemma ball_one_subset_slitPlane : Metric.ball 1 1 ⊆ slitPlane := fun z hz ↦ .inl <|
+  have : -1 < z.re - 1 := neg_lt_of_abs_lt <| (abs_re_le_abs _).trans_lt hz
+  by linarith
+
+/-- The slit plane includes the open unit ball of radius `1` around `1`. -/
+lemma mem_slitPlane_of_norm_lt_one {z : ℂ} (hz : ‖z‖ < 1) : 1 + z ∈ slitPlane :=
+  ball_one_subset_slitPlane <| by simpa
+
+end slitPlane
+
 end Complex

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -194,9 +194,8 @@ theorem nnnorm_int (n : ℤ) : ‖(n : ℂ)‖₊ = ‖n‖₊ :=
   Subtype.ext norm_int
 #align complex.nnnorm_int Complex.nnnorm_int
 
-theorem nnnorm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖₊ = 1 := by
-  refine' (@pow_left_inj NNReal _ _ _ _ zero_le' zero_le' hn.bot_lt).mp _
-  rw [← nnnorm_pow, h, nnnorm_one, one_pow]
+theorem nnnorm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖₊ = 1 :=
+  (pow_left_inj zero_le' zero_le' hn).1 $ by rw [← nnnorm_pow, h, nnnorm_one, one_pow]
 #align complex.nnnorm_eq_one_of_pow_eq_one Complex.nnnorm_eq_one_of_pow_eq_one
 
 theorem norm_eq_one_of_pow_eq_one {ζ : ℂ} {n : ℕ} (h : ζ ^ n = 1) (hn : n ≠ 0) : ‖ζ‖ = 1 :=

@@ -234,6 +234,9 @@ def equivRealProdClm : ℂ ≃L[ℝ] ℝ × ℝ :=
     abs_le_sqrt_two_mul_max (equivRealProd.symm p)
 #align complex.equiv_real_prod_clm Complex.equivRealProdClm
 
+theorem equivRealProdClm_symm_apply (p : ℝ × ℝ) :
+    Complex.equivRealProdClm.symm p = p.1 + p.2 * Complex.I := Complex.equivRealProd_symm_apply p
+
 instance : ProperSpace ℂ :=
   (id lipschitz_equivRealProd : LipschitzWith 1 equivRealProdClm.toHomeomorph).properSpace
 

Having _ofNat lemmas is important for confluence given that for both normSq and abs, the _ofReal lemma is @[simp] and so is ofReal_ofNat. We already have lemmas for 0 and 1 from the bundled classes for both functions, so I'm only adding lemmas for the AtLeastTwo case here.

@@ -158,7 +158,7 @@ theorem norm_rat (r : ℚ) : ‖(r : ℂ)‖ = |(r : ℝ)| := by
 
 @[simp 1100]
 theorem norm_nat (n : ℕ) : ‖(n : ℂ)‖ = n :=
-  abs_of_nat _
+  abs_natCast _
 #align complex.norm_nat Complex.norm_nat
 
 @[simp 1100]

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

This has nice performance benefits.

@@ -73,12 +73,12 @@ instance : DenselyNormedField ℂ where
     let ⟨x, h⟩ := exists_between hr
     ⟨x, by rwa [norm_eq_abs, abs_ofReal, abs_of_pos (h₀.trans_lt h.1)]⟩
 
-instance {R : Type _} [NormedField R] [NormedAlgebra R ℝ] : NormedAlgebra R ℂ where
+instance {R : Type*} [NormedField R] [NormedAlgebra R ℝ] : NormedAlgebra R ℂ where
   norm_smul_le r x := by
     rw [← algebraMap_smul ℝ r x, real_smul, norm_mul, norm_eq_abs, abs_ofReal, ← Real.norm_eq_abs,
       norm_algebraMap']
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℂ E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E]
 
 -- see Note [lower instance priority]
 /-- The module structure from `Module.complexToReal` is a normed space. -/
@@ -479,7 +479,7 @@ theorem normSq_to_complex {x : ℂ} : norm_sqC x = Complex.normSq x :=
 
 section tsum
 
-variable {α : Type _} (𝕜 : Type _) [IsROrC 𝕜]
+variable {α : Type*} (𝕜 : Type*) [IsROrC 𝕜]
 
 @[simp]
 theorem hasSum_conj {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x)) x ↔ HasSum f (conj x) :=
@@ -566,7 +566,7 @@ discoverability and to avoid the need to unify `𝕜`.
 
 section tsum
 
-variable {α : Type _}
+variable {α : Type*}
 
 open ComplexConjugate
 

With open scoped ComplexOrder, we current have StarOrderedRing Complex (as well as some other order instances). With this PR, that scope puts the same order on K where IsROrC K.

There is an ongoing discussion about whether opening the scope should be required, but there is no need to address that concern simultaneously with improving behavior when the scope is already open. There also seems to be fewer downstream instance resolution issues to resolve by leaving it in the scope.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -423,6 +423,8 @@ noncomputable instance : IsROrC ℂ where
   conj_I_ax := conj_I
   norm_sq_eq_def_ax z := (normSq_eq_abs z).symm
   mul_im_I_ax _ := mul_one _
+  toPartialOrder := Complex.partialOrder
+  le_iff_re_im := Iff.rfl
 
 theorem _root_.IsROrC.re_eq_complex_re : ⇑(IsROrC.re : ℂ →+ ℝ) = Complex.re :=
   rfl

Given how confusing this order could be to newcomers, it's probably not reasonable to call it Basic. At any rate, Data/Complex/Basic is very long, and this is an easy split.

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
 import Mathlib.Data.Complex.Module
+import Mathlib.Data.Complex.Order
 import Mathlib.Data.Complex.Exponential
 import Mathlib.Data.IsROrC.Basic
 import Mathlib.Topology.Algebra.InfiniteSum.Module

• 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) Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module analysis.complex.basic
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Complex.Module
 import Mathlib.Data.Complex.Exponential
@@ -14,6 +9,8 @@ import Mathlib.Data.IsROrC.Basic
 import Mathlib.Topology.Algebra.InfiniteSum.Module
 import Mathlib.Topology.Instances.RealVectorSpace
 
+#align_import analysis.complex.basic from "leanprover-community/mathlib"@"3f655f5297b030a87d641ad4e825af8d9679eb0b"
+
 /-!
 # Normed space structure on `ℂ`.
 

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -292,12 +292,12 @@ theorem imClm_apply (z : ℂ) : (imClm : ℂ → ℝ) z = z.im :=
   rfl
 #align complex.im_clm_apply Complex.imClm_apply
 
-theorem restrictScalars_one_smul_right' (x : E) :
+theorem restrictScalars_one_smulRight' (x : E) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smulRight x : ℂ →L[ℂ] E) =
       reClm.smulRight x + I • imClm.smulRight x := by
   ext ⟨a, b⟩
   simp [mk_eq_add_mul_I, mul_smul, smul_comm I b x]
-#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smul_right'
+#align complex.restrict_scalars_one_smul_right' Complex.restrictScalars_one_smulRight'
 
 theorem restrictScalars_one_smulRight (x : ℂ) :
     ContinuousLinearMap.restrictScalars ℝ ((1 : ℂ →L[ℂ] ℂ).smulRight x : ℂ →L[ℂ] ℂ) =

@@ -38,7 +38,7 @@ We also register the fact that `ℂ` is an `IsROrC` field.
 -/
 
 
--- porting note: todo: restore assert_not_exists Absorbs
+assert_not_exists Absorbs
 
 noncomputable section
 

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -490,7 +490,6 @@ theorem hasSum_conj' {f : α → 𝕜} {x : 𝕜} : HasSum (fun x => conj (f x))
   conjCle.hasSum'
 #align is_R_or_C.has_sum_conj' IsROrC.hasSum_conj'
 
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Summable f :=
   summable_star_iff
@@ -498,7 +497,6 @@ theorem summable_conj {f : α → 𝕜} : (Summable fun x => conj (f x)) ↔ Sum
 
 variable {𝕜}
 
-set_option synthInstance.etaExperiment true in
 theorem conj_tsum (f : α → 𝕜) : conj (∑' a, f a) = ∑' a, conj (f a) :=
   tsum_star
 #align is_R_or_C.conj_tsum IsROrC.conj_tsum

Co-authored-by: Yakov Pechersky <ypechersky@treeline.bio> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>