data.is_R_or_C.basic ⟷ Mathlib.Data.IsROrC.Basic

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

@@ -305,7 +305,7 @@ theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
     ((∏ i in s, f i : ℝ) : K) = ∏ i in s, (f i : K) :=
-  RingHom.map_prod _ _ _
+  map_prod _ _ _
 #align is_R_or_C.of_real_prod RCLike.ofReal_prod
 -/
 

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

@@ -51,11 +51,11 @@ local notation "𝓚" => algebraMap ℝ _
 
 open scoped ComplexConjugate
 
-#print IsROrC /-
+#print RCLike /-
 /--
 This typeclass captures properties shared by ℝ and ℂ, with an API that closely matches that of ℂ.
 -/
-class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebra ℝ K,
+class RCLike (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebra ℝ K,
     CompleteSpace K where
   re : K →+ ℝ
   im : K →+ ℝ
@@ -73,445 +73,429 @@ class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebr
   conj_i_ax : conj I = -I
   norm_sq_eq_def_ax : ∀ z : K, ‖z‖ ^ 2 = re z * re z + im z * im z
   hMul_im_i_ax : ∀ z : K, im z * im I = im z
-#align is_R_or_C IsROrC
+#align is_R_or_C RCLike
 -/
 
 end
 
-variable {K E : Type _} [IsROrC K]
+variable {K E : Type _} [RCLike K]
 
-namespace IsROrC
+namespace RCLike
 
 open scoped ComplexConjugate
 
-#print IsROrC.algebraMapCoe /-
+#print RCLike.algebraMapCoe /-
 /- The priority must be set at 900 to ensure that coercions are tried in the right order.
 See Note [coercion into rings], or `data/nat/cast.lean` for more details. -/
 noncomputable instance (priority := 900) algebraMapCoe : CoeTC ℝ K :=
   ⟨algebraMap ℝ K⟩
-#align is_R_or_C.algebra_map_coe IsROrC.algebraMapCoe
+#align is_R_or_C.algebra_map_coe RCLike.algebraMapCoe
 -/
 
-#print IsROrC.ofReal_alg /-
+#print RCLike.ofReal_alg /-
 theorem ofReal_alg (x : ℝ) : (x : K) = x • (1 : K) :=
   Algebra.algebraMap_eq_smul_one x
-#align is_R_or_C.of_real_alg IsROrC.ofReal_alg
+#align is_R_or_C.of_real_alg RCLike.ofReal_alg
 -/
 
-#print IsROrC.real_smul_eq_coe_mul /-
+#print RCLike.real_smul_eq_coe_mul /-
 theorem real_smul_eq_coe_mul (r : ℝ) (z : K) : r • z = (r : K) * z :=
   Algebra.smul_def r z
-#align is_R_or_C.real_smul_eq_coe_mul IsROrC.real_smul_eq_coe_mul
+#align is_R_or_C.real_smul_eq_coe_mul RCLike.real_smul_eq_coe_mul
 -/
 
-#print IsROrC.real_smul_eq_coe_smul /-
+#print RCLike.real_smul_eq_coe_smul /-
 theorem real_smul_eq_coe_smul [AddCommGroup E] [Module K E] [Module ℝ E] [IsScalarTower ℝ K E]
-    (r : ℝ) (x : E) : r • x = (r : K) • x := by rw [IsROrC.ofReal_alg, smul_one_smul]
-#align is_R_or_C.real_smul_eq_coe_smul IsROrC.real_smul_eq_coe_smul
+    (r : ℝ) (x : E) : r • x = (r : K) • x := by rw [RCLike.ofReal_alg, smul_one_smul]
+#align is_R_or_C.real_smul_eq_coe_smul RCLike.real_smul_eq_coe_smul
 -/
 
-#print IsROrC.algebraMap_eq_ofReal /-
+#print RCLike.algebraMap_eq_ofReal /-
 theorem algebraMap_eq_ofReal : ⇑(algebraMap ℝ K) = coe :=
   rfl
-#align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_ofReal
+#align is_R_or_C.algebra_map_eq_of_real RCLike.algebraMap_eq_ofReal
 -/
 
-#print IsROrC.re_add_im /-
+#print RCLike.re_add_im /-
 @[simp, is_R_or_C_simps]
 theorem re_add_im (z : K) : (re z : K) + im z * i = z :=
-  IsROrC.re_add_im_ax z
-#align is_R_or_C.re_add_im IsROrC.re_add_im
+  RCLike.re_add_im_ax z
+#align is_R_or_C.re_add_im RCLike.re_add_im
 -/
 
-#print IsROrC.ofReal_re /-
+#print RCLike.ofReal_re /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_re : ∀ r : ℝ, re (r : K) = r :=
-  IsROrC.of_real_re_ax
-#align is_R_or_C.of_real_re IsROrC.ofReal_re
+  RCLike.of_real_re_ax
+#align is_R_or_C.of_real_re RCLike.ofReal_re
 -/
 
-#print IsROrC.ofReal_im /-
+#print RCLike.ofReal_im /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_im : ∀ r : ℝ, im (r : K) = 0 :=
-  IsROrC.of_real_im_ax
-#align is_R_or_C.of_real_im IsROrC.ofReal_im
+  RCLike.of_real_im_ax
+#align is_R_or_C.of_real_im RCLike.ofReal_im
 -/
 
-#print IsROrC.mul_re /-
+#print RCLike.mul_re /-
 @[simp, is_R_or_C_simps]
 theorem mul_re : ∀ z w : K, re (z * w) = re z * re w - im z * im w :=
-  IsROrC.hMul_re_ax
-#align is_R_or_C.mul_re IsROrC.mul_re
+  RCLike.hMul_re_ax
+#align is_R_or_C.mul_re RCLike.mul_re
 -/
 
-#print IsROrC.mul_im /-
+#print RCLike.mul_im /-
 @[simp, is_R_or_C_simps]
 theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
-  IsROrC.hMul_im_ax
-#align is_R_or_C.mul_im IsROrC.mul_im
+  RCLike.hMul_im_ax
+#align is_R_or_C.mul_im RCLike.mul_im
 -/
 
-#print IsROrC.ext_iff /-
+#print RCLike.ext_iff /-
 theorem ext_iff {z w : K} : z = w ↔ re z = re w ∧ im z = im w :=
   ⟨fun h => h ▸ ⟨rfl, rfl⟩, fun ⟨h₁, h₂⟩ => re_add_im z ▸ re_add_im w ▸ h₁ ▸ h₂ ▸ rfl⟩
-#align is_R_or_C.ext_iff IsROrC.ext_iff
+#align is_R_or_C.ext_iff RCLike.ext_iff
 -/
 
-#print IsROrC.ext /-
+#print RCLike.ext /-
 theorem ext {z w : K} (hre : re z = re w) (him : im z = im w) : z = w :=
   ext_iff.2 ⟨hre, him⟩
-#align is_R_or_C.ext IsROrC.ext
+#align is_R_or_C.ext RCLike.ext
 -/
 
-#print IsROrC.ofReal_zero /-
+#print RCLike.ofReal_zero /-
 @[norm_cast]
 theorem ofReal_zero : ((0 : ℝ) : K) = 0 :=
   algebraMap.coe_zero
-#align is_R_or_C.of_real_zero IsROrC.ofReal_zero
+#align is_R_or_C.of_real_zero RCLike.ofReal_zero
 -/
 
-#print IsROrC.zero_re' /-
+#print RCLike.zero_re' /-
 @[is_R_or_C_simps]
 theorem zero_re' : re (0 : K) = (0 : ℝ) :=
   map_zero re
-#align is_R_or_C.zero_re' IsROrC.zero_re'
+#align is_R_or_C.zero_re' RCLike.zero_re'
 -/
 
-#print IsROrC.ofReal_one /-
+#print RCLike.ofReal_one /-
 @[norm_cast]
 theorem ofReal_one : ((1 : ℝ) : K) = 1 :=
   map_one (algebraMap ℝ K)
-#align is_R_or_C.of_real_one IsROrC.ofReal_one
+#align is_R_or_C.of_real_one RCLike.ofReal_one
 -/
 
-#print IsROrC.one_re /-
+#print RCLike.one_re /-
 @[simp, is_R_or_C_simps]
 theorem one_re : re (1 : K) = 1 := by rw [← of_real_one, of_real_re]
-#align is_R_or_C.one_re IsROrC.one_re
+#align is_R_or_C.one_re RCLike.one_re
 -/
 
-#print IsROrC.one_im /-
+#print RCLike.one_im /-
 @[simp, is_R_or_C_simps]
 theorem one_im : im (1 : K) = 0 := by rw [← of_real_one, of_real_im]
-#align is_R_or_C.one_im IsROrC.one_im
+#align is_R_or_C.one_im RCLike.one_im
 -/
 
-#print IsROrC.ofReal_injective /-
+#print RCLike.ofReal_injective /-
 theorem ofReal_injective : Function.Injective (coe : ℝ → K) :=
   (algebraMap ℝ K).Injective
-#align is_R_or_C.of_real_injective IsROrC.ofReal_injective
+#align is_R_or_C.of_real_injective RCLike.ofReal_injective
 -/
 
-#print IsROrC.ofReal_inj /-
+#print RCLike.ofReal_inj /-
 @[norm_cast]
 theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
   algebraMap.coe_inj
-#align is_R_or_C.of_real_inj IsROrC.ofReal_inj
+#align is_R_or_C.of_real_inj RCLike.ofReal_inj
 -/
 
-#print IsROrC.bit0_re /-
 @[simp, is_R_or_C_simps]
 theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
   map_bit0 _ _
-#align is_R_or_C.bit0_re IsROrC.bit0_re
--/
+#align is_R_or_C.bit0_re RCLike.bit0_re
 
-#print IsROrC.bit1_re /-
 @[simp, is_R_or_C_simps]
 theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_add, bit0_re, one_re]
-#align is_R_or_C.bit1_re IsROrC.bit1_re
--/
+#align is_R_or_C.bit1_re RCLike.bit1_re
 
-#print IsROrC.bit0_im /-
 @[simp, is_R_or_C_simps]
 theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
   map_bit0 _ _
-#align is_R_or_C.bit0_im IsROrC.bit0_im
--/
+#align is_R_or_C.bit0_im RCLike.bit0_im
 
-#print IsROrC.bit1_im /-
 @[simp, is_R_or_C_simps]
 theorem bit1_im (z : K) : im (bit1 z) = bit0 (im z) := by
   simp only [bit1, map_add, bit0_im, one_im, add_zero]
-#align is_R_or_C.bit1_im IsROrC.bit1_im
--/
+#align is_R_or_C.bit1_im RCLike.bit1_im
 
-#print IsROrC.ofReal_eq_zero /-
+#print RCLike.ofReal_eq_zero /-
 theorem ofReal_eq_zero {x : ℝ} : (x : K) = 0 ↔ x = 0 :=
   algebraMap.lift_map_eq_zero_iff x
-#align is_R_or_C.of_real_eq_zero IsROrC.ofReal_eq_zero
+#align is_R_or_C.of_real_eq_zero RCLike.ofReal_eq_zero
 -/
 
-#print IsROrC.ofReal_ne_zero /-
+#print RCLike.ofReal_ne_zero /-
 theorem ofReal_ne_zero {x : ℝ} : (x : K) ≠ 0 ↔ x ≠ 0 :=
   ofReal_eq_zero.Not
-#align is_R_or_C.of_real_ne_zero IsROrC.ofReal_ne_zero
+#align is_R_or_C.of_real_ne_zero RCLike.ofReal_ne_zero
 -/
 
-#print IsROrC.ofReal_add /-
+#print RCLike.ofReal_add /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : K) = r + s :=
   algebraMap.coe_add _ _
-#align is_R_or_C.of_real_add IsROrC.ofReal_add
+#align is_R_or_C.of_real_add RCLike.ofReal_add
 -/
 
-#print IsROrC.ofReal_bit0 /-
 @[simp, is_R_or_C_simps, norm_cast]
-theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
+theorem of_real_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
   ofReal_add _ _
-#align is_R_or_C.of_real_bit0 IsROrC.ofReal_bit0
--/
+#align is_R_or_C.of_real_bit0 RCLike.of_real_bit0
 
-#print IsROrC.ofReal_bit1 /-
 @[simp, is_R_or_C_simps, norm_cast]
-theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
+theorem of_real_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
   map_bit1 (algebraMap ℝ K) r
-#align is_R_or_C.of_real_bit1 IsROrC.ofReal_bit1
--/
+#align is_R_or_C.of_real_bit1 RCLike.of_real_bit1
 
-#print IsROrC.ofReal_neg /-
+#print RCLike.ofReal_neg /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : K) = -r :=
   algebraMap.coe_neg r
-#align is_R_or_C.of_real_neg IsROrC.ofReal_neg
+#align is_R_or_C.of_real_neg RCLike.ofReal_neg
 -/
 
-#print IsROrC.ofReal_sub /-
+#print RCLike.ofReal_sub /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
   map_sub (algebraMap ℝ K) r s
-#align is_R_or_C.of_real_sub IsROrC.ofReal_sub
+#align is_R_or_C.of_real_sub RCLike.ofReal_sub
 -/
 
-#print IsROrC.ofReal_sum /-
+#print RCLike.ofReal_sum /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_sum {α : Type _} (s : Finset α) (f : α → ℝ) :
     ((∑ i in s, f i : ℝ) : K) = ∑ i in s, (f i : K) :=
   map_sum (algebraMap ℝ K) _ _
-#align is_R_or_C.of_real_sum IsROrC.ofReal_sum
+#align is_R_or_C.of_real_sum RCLike.ofReal_sum
 -/
 
-#print IsROrC.ofReal_finsupp_sum /-
+#print RCLike.ofReal_finsupp_sum /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_finsupp_sum {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.Sum fun a b => g a b : ℝ) : K) = f.Sum fun a b => (g a b : K) :=
   map_finsupp_sum (algebraMap ℝ K) f g
-#align is_R_or_C.of_real_finsupp_sum IsROrC.ofReal_finsupp_sum
+#align is_R_or_C.of_real_finsupp_sum RCLike.ofReal_finsupp_sum
 -/
 
-#print IsROrC.ofReal_mul /-
+#print RCLike.ofReal_mul /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : K) = r * s :=
   algebraMap.coe_mul _ _
-#align is_R_or_C.of_real_mul IsROrC.ofReal_mul
+#align is_R_or_C.of_real_mul RCLike.ofReal_mul
 -/
 
-#print IsROrC.ofReal_pow /-
+#print RCLike.ofReal_pow /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
   map_pow (algebraMap ℝ K) r n
-#align is_R_or_C.of_real_pow IsROrC.ofReal_pow
+#align is_R_or_C.of_real_pow RCLike.ofReal_pow
 -/
 
-#print IsROrC.ofReal_prod /-
+#print RCLike.ofReal_prod /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
     ((∏ i in s, f i : ℝ) : K) = ∏ i in s, (f i : K) :=
   RingHom.map_prod _ _ _
-#align is_R_or_C.of_real_prod IsROrC.ofReal_prod
+#align is_R_or_C.of_real_prod RCLike.ofReal_prod
 -/
 
-#print IsROrC.ofReal_finsupp_prod /-
+#print RCLike.ofReal_finsupp_prod /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.Prod fun a b => g a b : ℝ) : K) = f.Prod fun a b => (g a b : K) :=
   RingHom.map_finsupp_prod _ f g
-#align is_R_or_C.of_real_finsupp_prod IsROrC.ofReal_finsupp_prod
+#align is_R_or_C.of_real_finsupp_prod RCLike.ofReal_finsupp_prod
 -/
 
-#print IsROrC.real_smul_ofReal /-
+#print RCLike.real_smul_ofReal /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem real_smul_ofReal (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
   real_smul_eq_coe_mul _ _
-#align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofReal
+#align is_R_or_C.real_smul_of_real RCLike.real_smul_ofReal
 -/
 
-#print IsROrC.re_ofReal_mul /-
+#print RCLike.re_ofReal_mul /-
 @[is_R_or_C_simps]
 theorem re_ofReal_mul (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
   simp only [mul_re, of_real_im, MulZeroClass.zero_mul, of_real_re, sub_zero]
-#align is_R_or_C.of_real_mul_re IsROrC.re_ofReal_mul
+#align is_R_or_C.of_real_mul_re RCLike.re_ofReal_mul
 -/
 
-#print IsROrC.im_ofReal_mul /-
+#print RCLike.im_ofReal_mul /-
 @[is_R_or_C_simps]
 theorem im_ofReal_mul (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
   simp only [add_zero, of_real_im, MulZeroClass.zero_mul, of_real_re, mul_im]
-#align is_R_or_C.of_real_mul_im IsROrC.im_ofReal_mul
+#align is_R_or_C.of_real_mul_im RCLike.im_ofReal_mul
 -/
 
-#print IsROrC.smul_re /-
+#print RCLike.smul_re /-
 @[is_R_or_C_simps]
 theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
   rw [real_smul_eq_coe_mul, of_real_mul_re]
-#align is_R_or_C.smul_re IsROrC.smul_re
+#align is_R_or_C.smul_re RCLike.smul_re
 -/
 
-#print IsROrC.smul_im /-
+#print RCLike.smul_im /-
 @[is_R_or_C_simps]
 theorem smul_im (r : ℝ) (z : K) : im (r • z) = r * im z := by
   rw [real_smul_eq_coe_mul, of_real_mul_im]
-#align is_R_or_C.smul_im IsROrC.smul_im
+#align is_R_or_C.smul_im RCLike.smul_im
 -/
 
-#print IsROrC.norm_ofReal /-
+#print RCLike.norm_ofReal /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem norm_ofReal (r : ℝ) : ‖(r : K)‖ = |r| :=
   norm_algebraMap' K r
-#align is_R_or_C.norm_of_real IsROrC.norm_ofReal
+#align is_R_or_C.norm_of_real RCLike.norm_ofReal
 -/
 
 /-! ### Characteristic zero -/
 
 
-#print IsROrC.charZero_isROrC /-
+#print RCLike.charZero_rclike /-
 -- see Note [lower instance priority]
 /-- ℝ and ℂ are both of characteristic zero.  -/
-instance (priority := 100) charZero_isROrC : CharZero K :=
+instance (priority := 100) charZero_rclike : CharZero K :=
   (RingHom.charZero_iff (algebraMap ℝ K).Injective).1 inferInstance
-#align is_R_or_C.char_zero_R_or_C IsROrC.charZero_isROrC
+#align is_R_or_C.char_zero_R_or_C RCLike.charZero_rclike
 -/
 
 /-! ### The imaginary unit, `I` -/
 
 
-#print IsROrC.I_re /-
+#print RCLike.I_re /-
 /-- The imaginary unit. -/
 @[simp, is_R_or_C_simps]
 theorem I_re : re (i : K) = 0 :=
   i_re_ax
-#align is_R_or_C.I_re IsROrC.I_re
+#align is_R_or_C.I_re RCLike.I_re
 -/
 
-#print IsROrC.I_im /-
+#print RCLike.I_im /-
 @[simp, is_R_or_C_simps]
 theorem I_im (z : K) : im z * im (i : K) = im z :=
   hMul_im_i_ax z
-#align is_R_or_C.I_im IsROrC.I_im
+#align is_R_or_C.I_im RCLike.I_im
 -/
 
-#print IsROrC.I_im' /-
+#print RCLike.I_im' /-
 @[simp, is_R_or_C_simps]
 theorem I_im' (z : K) : im (i : K) * im z = im z := by rw [mul_comm, I_im _]
-#align is_R_or_C.I_im' IsROrC.I_im'
+#align is_R_or_C.I_im' RCLike.I_im'
 -/
 
-#print IsROrC.I_mul_re /-
+#print RCLike.I_mul_re /-
 @[simp, is_R_or_C_simps]
 theorem I_mul_re (z : K) : re (i * z) = -im z := by
   simp only [I_re, zero_sub, I_im', MulZeroClass.zero_mul, mul_re]
-#align is_R_or_C.I_mul_re IsROrC.I_mul_re
+#align is_R_or_C.I_mul_re RCLike.I_mul_re
 -/
 
-#print IsROrC.I_mul_I /-
+#print RCLike.I_mul_I /-
 theorem I_mul_I : (i : K) = 0 ∨ (i : K) * i = -1 :=
   i_hMul_i_ax
-#align is_R_or_C.I_mul_I IsROrC.I_mul_I
+#align is_R_or_C.I_mul_I RCLike.I_mul_I
 -/
 
-#print IsROrC.conj_re /-
+#print RCLike.conj_re /-
 @[simp, is_R_or_C_simps]
 theorem conj_re (z : K) : re (conj z) = re z :=
-  IsROrC.conj_re_ax z
-#align is_R_or_C.conj_re IsROrC.conj_re
+  RCLike.conj_re_ax z
+#align is_R_or_C.conj_re RCLike.conj_re
 -/
 
-#print IsROrC.conj_im /-
+#print RCLike.conj_im /-
 @[simp, is_R_or_C_simps]
 theorem conj_im (z : K) : im (conj z) = -im z :=
-  IsROrC.conj_im_ax z
-#align is_R_or_C.conj_im IsROrC.conj_im
+  RCLike.conj_im_ax z
+#align is_R_or_C.conj_im RCLike.conj_im
 -/
 
-#print IsROrC.conj_I /-
+#print RCLike.conj_I /-
 @[simp, is_R_or_C_simps]
 theorem conj_I : conj (i : K) = -i :=
-  IsROrC.conj_i_ax
-#align is_R_or_C.conj_I IsROrC.conj_I
+  RCLike.conj_i_ax
+#align is_R_or_C.conj_I RCLike.conj_I
 -/
 
-#print IsROrC.conj_ofReal /-
+#print RCLike.conj_ofReal /-
 @[simp, is_R_or_C_simps]
 theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) := by rw [ext_iff];
   simp only [of_real_im, conj_im, eq_self_iff_true, conj_re, and_self_iff, neg_zero]
-#align is_R_or_C.conj_of_real IsROrC.conj_ofReal
+#align is_R_or_C.conj_of_real RCLike.conj_ofReal
 -/
 
-#print IsROrC.conj_bit0 /-
 @[simp, is_R_or_C_simps]
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
   map_bit0 _ _
-#align is_R_or_C.conj_bit0 IsROrC.conj_bit0
--/
+#align is_R_or_C.conj_bit0 RCLike.conj_bit0
 
-#print IsROrC.conj_bit1 /-
 @[simp, is_R_or_C_simps]
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
   map_bit1 _ _
-#align is_R_or_C.conj_bit1 IsROrC.conj_bit1
--/
+#align is_R_or_C.conj_bit1 RCLike.conj_bit1
 
-#print IsROrC.conj_neg_I /-
+#print RCLike.conj_neg_I /-
 @[simp, is_R_or_C_simps]
 theorem conj_neg_I : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
-#align is_R_or_C.conj_neg_I IsROrC.conj_neg_I
+#align is_R_or_C.conj_neg_I RCLike.conj_neg_I
 -/
 
-#print IsROrC.conj_eq_re_sub_im /-
+#print RCLike.conj_eq_re_sub_im /-
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
   (congr_arg conj (re_add_im z).symm).trans <| by
     rw [map_add, map_mul, conj_I, conj_of_real, conj_of_real, mul_neg, sub_eq_add_neg]
-#align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_im
+#align is_R_or_C.conj_eq_re_sub_im RCLike.conj_eq_re_sub_im
 -/
 
-#print IsROrC.sub_conj /-
+#print RCLike.sub_conj /-
 theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
   by
   nth_rw 1 [← re_add_im z]
   rw [conj_eq_re_sub_im, add_sub_sub_cancel, ← two_mul, mul_assoc]
-#align is_R_or_C.sub_conj IsROrC.sub_conj
+#align is_R_or_C.sub_conj RCLike.sub_conj
 -/
 
-#print IsROrC.conj_smul /-
+#print RCLike.conj_smul /-
 @[is_R_or_C_simps]
 theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
   rw [conj_eq_re_sub_im, conj_eq_re_sub_im, smul_re, smul_im, of_real_mul, of_real_mul,
     real_smul_eq_coe_mul, mul_sub, mul_assoc]
-#align is_R_or_C.conj_smul IsROrC.conj_smul
+#align is_R_or_C.conj_smul RCLike.conj_smul
 -/
 
-#print IsROrC.add_conj /-
+#print RCLike.add_conj /-
 theorem add_conj (z : K) : z + conj z = 2 * re z :=
   calc
     z + conj z = re z + im z * i + (re z - im z * i) := by rw [re_add_im, conj_eq_re_sub_im]
     _ = 2 * re z := by rw [add_add_sub_cancel, two_mul]
-#align is_R_or_C.add_conj IsROrC.add_conj
+#align is_R_or_C.add_conj RCLike.add_conj
 -/
 
-#print IsROrC.re_eq_add_conj /-
+#print RCLike.re_eq_add_conj /-
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
-  rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
-#align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
+  rw [add_conj, mul_div_cancel_left₀ (re z : K) two_ne_zero]
+#align is_R_or_C.re_eq_add_conj RCLike.re_eq_add_conj
 -/
 
-#print IsROrC.im_eq_conj_sub /-
+#print RCLike.im_eq_conj_sub /-
 theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
   rw [← neg_inj, ← of_real_neg, ← I_mul_re, re_eq_add_conj, map_mul, conj_I, ← neg_div, ← mul_neg,
     neg_sub, mul_sub, neg_mul, sub_eq_add_neg]
-#align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_sub
+#align is_R_or_C.im_eq_conj_sub RCLike.im_eq_conj_sub
 -/
 
-#print IsROrC.is_real_TFAE /-
+#print RCLike.is_real_TFAE /-
 /-- There are several equivalent ways to say that a number `z` is in fact a real number. -/
 theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] :=
   by
@@ -525,182 +509,182 @@ theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(r
   tfae_have 3 → 2; exact fun h => ⟨_, h⟩
   tfae_have 2 → 1; exact fun ⟨r, hr⟩ => hr ▸ conj_of_real _
   tfae_finish
-#align is_R_or_C.is_real_tfae IsROrC.is_real_TFAE
+#align is_R_or_C.is_real_tfae RCLike.is_real_TFAE
 -/
 
-#print IsROrC.conj_eq_iff_real /-
+#print RCLike.conj_eq_iff_real /-
 theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
   ((is_real_TFAE z).out 0 1).trans <| by simp only [eq_comm]
-#align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_real
+#align is_R_or_C.conj_eq_iff_real RCLike.conj_eq_iff_real
 -/
 
-#print IsROrC.conj_eq_iff_re /-
+#print RCLike.conj_eq_iff_re /-
 theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
   (is_real_TFAE z).out 0 2
-#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
+#align is_R_or_C.conj_eq_iff_re RCLike.conj_eq_iff_re
 -/
 
-#print IsROrC.conj_eq_iff_im /-
+#print RCLike.conj_eq_iff_im /-
 theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
   (is_real_TFAE z).out 0 3
-#align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_im
+#align is_R_or_C.conj_eq_iff_im RCLike.conj_eq_iff_im
 -/
 
-#print IsROrC.star_def /-
+#print RCLike.star_def /-
 @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
   rfl
-#align is_R_or_C.star_def IsROrC.star_def
+#align is_R_or_C.star_def RCLike.star_def
 -/
 
 variable (K)
 
-#print IsROrC.conjToRingEquiv /-
+#print RCLike.conjToRingEquiv /-
 /-- Conjugation as a ring equivalence. This is used to convert the inner product into a
 sesquilinear product. -/
 abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
   starRingEquiv
-#align is_R_or_C.conj_to_ring_equiv IsROrC.conjToRingEquiv
+#align is_R_or_C.conj_to_ring_equiv RCLike.conjToRingEquiv
 -/
 
 variable {K}
 
-#print IsROrC.normSq /-
+#print RCLike.normSq /-
 /-- The norm squared function. -/
 def normSq : K →*₀ ℝ where
   toFun z := re z * re z + im z * im z
   map_zero' := by simp only [add_zero, MulZeroClass.mul_zero, map_zero]
   map_one' := by simp only [one_im, add_zero, mul_one, one_re, MulZeroClass.mul_zero]
   map_mul' z w := by simp only [mul_im, mul_re]; ring
-#align is_R_or_C.norm_sq IsROrC.normSq
+#align is_R_or_C.norm_sq RCLike.normSq
 -/
 
-#print IsROrC.normSq_apply /-
+#print RCLike.normSq_apply /-
 theorem normSq_apply (z : K) : normSq z = re z * re z + im z * im z :=
   rfl
-#align is_R_or_C.norm_sq_apply IsROrC.normSq_apply
+#align is_R_or_C.norm_sq_apply RCLike.normSq_apply
 -/
 
-#print IsROrC.norm_sq_eq_def /-
+#print RCLike.norm_sq_eq_def /-
 theorem norm_sq_eq_def {z : K} : ‖z‖ ^ 2 = re z * re z + im z * im z :=
   norm_sq_eq_def_ax z
-#align is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_def
+#align is_R_or_C.norm_sq_eq_def RCLike.norm_sq_eq_def
 -/
 
-#print IsROrC.normSq_eq_def' /-
+#print RCLike.normSq_eq_def' /-
 theorem normSq_eq_def' (z : K) : normSq z = ‖z‖ ^ 2 :=
   norm_sq_eq_def.symm
-#align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'
+#align is_R_or_C.norm_sq_eq_def' RCLike.normSq_eq_def'
 -/
 
-#print IsROrC.normSq_zero /-
+#print RCLike.normSq_zero /-
 @[is_R_or_C_simps]
 theorem normSq_zero : normSq (0 : K) = 0 :=
   normSq.map_zero
-#align is_R_or_C.norm_sq_zero IsROrC.normSq_zero
+#align is_R_or_C.norm_sq_zero RCLike.normSq_zero
 -/
 
-#print IsROrC.normSq_one /-
+#print RCLike.normSq_one /-
 @[is_R_or_C_simps]
 theorem normSq_one : normSq (1 : K) = 1 :=
   normSq.map_one
-#align is_R_or_C.norm_sq_one IsROrC.normSq_one
+#align is_R_or_C.norm_sq_one RCLike.normSq_one
 -/
 
-#print IsROrC.normSq_nonneg /-
+#print RCLike.normSq_nonneg /-
 theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
   add_nonneg (hMul_self_nonneg _) (hMul_self_nonneg _)
-#align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonneg
+#align is_R_or_C.norm_sq_nonneg RCLike.normSq_nonneg
 -/
 
-#print IsROrC.normSq_eq_zero /-
+#print RCLike.normSq_eq_zero /-
 @[simp, is_R_or_C_simps]
 theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 := by rw [norm_sq_eq_def']; simp [sq]
-#align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zero
+#align is_R_or_C.norm_sq_eq_zero RCLike.normSq_eq_zero
 -/
 
-#print IsROrC.normSq_pos /-
+#print RCLike.normSq_pos /-
 @[simp, is_R_or_C_simps]
 theorem normSq_pos {z : K} : 0 < normSq z ↔ z ≠ 0 := by
   rw [lt_iff_le_and_ne, Ne, eq_comm] <;> simp [norm_sq_nonneg]
-#align is_R_or_C.norm_sq_pos IsROrC.normSq_pos
+#align is_R_or_C.norm_sq_pos RCLike.normSq_pos
 -/
 
-#print IsROrC.normSq_neg /-
+#print RCLike.normSq_neg /-
 @[simp, is_R_or_C_simps]
 theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [norm_sq_eq_def', norm_neg]
-#align is_R_or_C.norm_sq_neg IsROrC.normSq_neg
+#align is_R_or_C.norm_sq_neg RCLike.normSq_neg
 -/
 
-#print IsROrC.normSq_conj /-
+#print RCLike.normSq_conj /-
 @[simp, is_R_or_C_simps]
 theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
   simp only [norm_sq_apply, neg_mul, mul_neg, neg_neg, is_R_or_C_simps]
-#align is_R_or_C.norm_sq_conj IsROrC.normSq_conj
+#align is_R_or_C.norm_sq_conj RCLike.normSq_conj
 -/
 
-#print IsROrC.normSq_mul /-
+#print RCLike.normSq_mul /-
 @[simp, is_R_or_C_simps]
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_hMul z w
-#align is_R_or_C.norm_sq_mul IsROrC.normSq_mul
+#align is_R_or_C.norm_sq_mul RCLike.normSq_mul
 -/
 
-#print IsROrC.normSq_add /-
+#print RCLike.normSq_add /-
 theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) := by
   simp only [norm_sq_apply, map_add, mul_neg, sub_neg_eq_add, is_R_or_C_simps]; ring
-#align is_R_or_C.norm_sq_add IsROrC.normSq_add
+#align is_R_or_C.norm_sq_add RCLike.normSq_add
 -/
 
-#print IsROrC.re_sq_le_normSq /-
+#print RCLike.re_sq_le_normSq /-
 theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
   le_add_of_nonneg_right (hMul_self_nonneg _)
-#align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSq
+#align is_R_or_C.re_sq_le_norm_sq RCLike.re_sq_le_normSq
 -/
 
-#print IsROrC.im_sq_le_normSq /-
+#print RCLike.im_sq_le_normSq /-
 theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
   le_add_of_nonneg_left (hMul_self_nonneg _)
-#align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
+#align is_R_or_C.im_sq_le_norm_sq RCLike.im_sq_le_normSq
 -/
 
-#print IsROrC.mul_conj /-
+#print RCLike.mul_conj /-
 theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
   simp only [map_add, add_zero, ext_iff, add_left_inj, mul_eq_mul_left_iff, MulZeroClass.zero_mul,
     add_comm, true_or_iff, eq_self_iff_true, mul_neg, add_right_neg, zero_add, norm_sq_apply,
     mul_comm, and_self_iff, neg_neg, MulZeroClass.mul_zero, sub_eq_neg_add, neg_zero,
     is_R_or_C_simps]
-#align is_R_or_C.mul_conj IsROrC.mul_conj
+#align is_R_or_C.mul_conj RCLike.mul_conj
 -/
 
-#print IsROrC.conj_mul /-
+#print RCLike.conj_mul /-
 theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
-#align is_R_or_C.conj_mul IsROrC.conj_mul
+#align is_R_or_C.conj_mul RCLike.conj_mul
 -/
 
-#print IsROrC.normSq_sub /-
+#print RCLike.normSq_sub /-
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [norm_sq_add, sub_eq_add_neg, RingEquiv.map_neg, mul_neg, norm_sq_neg, map_neg]
-#align is_R_or_C.norm_sq_sub IsROrC.normSq_sub
+#align is_R_or_C.norm_sq_sub RCLike.normSq_sub
 -/
 
-#print IsROrC.sqrt_normSq_eq_norm /-
+#print RCLike.sqrt_normSq_eq_norm /-
 theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
   rw [norm_sq_eq_def', Real.sqrt_sq (norm_nonneg _)]
-#align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_norm
+#align is_R_or_C.sqrt_norm_sq_eq_norm RCLike.sqrt_normSq_eq_norm
 -/
 
 /-! ### Inversion -/
 
 
-#print IsROrC.ofReal_inv /-
+#print RCLike.ofReal_inv /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = r⁻¹ :=
   map_inv₀ (algebraMap ℝ K) r
-#align is_R_or_C.of_real_inv IsROrC.ofReal_inv
+#align is_R_or_C.of_real_inv RCLike.ofReal_inv
 -/
 
-#print IsROrC.inv_def /-
+#print RCLike.inv_def /-
 theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
   by
   rcases eq_or_ne z 0 with (rfl | h₀)
@@ -708,103 +692,103 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
   · apply inv_eq_of_mul_eq_one_right
     rw [← mul_assoc, mul_conj, of_real_inv, ← norm_sq_eq_def', mul_inv_cancel]
     rwa [of_real_ne_zero, Ne.def, norm_sq_eq_zero]
-#align is_R_or_C.inv_def IsROrC.inv_def
+#align is_R_or_C.inv_def RCLike.inv_def
 -/
 
-#print IsROrC.inv_re /-
+#print RCLike.inv_re /-
 @[simp, is_R_or_C_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
   rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_re, conj_re, div_eq_inv_mul]
-#align is_R_or_C.inv_re IsROrC.inv_re
+#align is_R_or_C.inv_re RCLike.inv_re
 -/
 
-#print IsROrC.inv_im /-
+#print RCLike.inv_im /-
 @[simp, is_R_or_C_simps]
 theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
   rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_im, conj_im, div_eq_inv_mul]
-#align is_R_or_C.inv_im IsROrC.inv_im
+#align is_R_or_C.inv_im RCLike.inv_im
 -/
 
-#print IsROrC.div_re /-
+#print RCLike.div_re /-
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, neg_mul, mul_neg, neg_neg, map_neg,
     is_R_or_C_simps]
-#align is_R_or_C.div_re IsROrC.div_re
+#align is_R_or_C.div_re RCLike.div_re
 -/
 
-#print IsROrC.div_im /-
+#print RCLike.div_im /-
 theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm, neg_mul, mul_neg, map_neg,
     is_R_or_C_simps]
-#align is_R_or_C.div_im IsROrC.div_im
+#align is_R_or_C.div_im RCLike.div_im
 -/
 
-#print IsROrC.conj_inv /-
+#print RCLike.conj_inv /-
 @[simp, is_R_or_C_simps]
 theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
-#align is_R_or_C.conj_inv IsROrC.conj_inv
+#align is_R_or_C.conj_inv RCLike.conj_inv
 -/
 
-#print IsROrC.ofReal_div /-
+#print RCLike.ofReal_div /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
   map_div₀ (algebraMap ℝ K) r s
-#align is_R_or_C.of_real_div IsROrC.ofReal_div
+#align is_R_or_C.of_real_div RCLike.ofReal_div
 -/
 
-#print IsROrC.div_re_ofReal /-
+#print RCLike.div_re_ofReal /-
 theorem div_re_ofReal {z : K} {r : ℝ} : re (z / r) = re z / r := by
   rw [div_eq_inv_mul, div_eq_inv_mul, ← of_real_inv, of_real_mul_re]
-#align is_R_or_C.div_re_of_real IsROrC.div_re_ofReal
+#align is_R_or_C.div_re_of_real RCLike.div_re_ofReal
 -/
 
-#print IsROrC.ofReal_zpow /-
+#print RCLike.ofReal_zpow /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : K) = r ^ n :=
   map_zpow₀ (algebraMap ℝ K) r n
-#align is_R_or_C.of_real_zpow IsROrC.ofReal_zpow
+#align is_R_or_C.of_real_zpow RCLike.ofReal_zpow
 -/
 
-#print IsROrC.I_mul_I_of_nonzero /-
+#print RCLike.I_mul_I_of_nonzero /-
 theorem I_mul_I_of_nonzero : (i : K) ≠ 0 → (i : K) * i = -1 :=
   i_hMul_i_ax.resolve_left
-#align is_R_or_C.I_mul_I_of_nonzero IsROrC.I_mul_I_of_nonzero
+#align is_R_or_C.I_mul_I_of_nonzero RCLike.I_mul_I_of_nonzero
 -/
 
-#print IsROrC.inv_I /-
+#print RCLike.inv_I /-
 @[simp, is_R_or_C_simps]
 theorem inv_I : (i : K)⁻¹ = -i := by
   by_cases h : (I : K) = 0
   · simp [h]
   · field_simp [I_mul_I_of_nonzero h]
-#align is_R_or_C.inv_I IsROrC.inv_I
+#align is_R_or_C.inv_I RCLike.inv_I
 -/
 
-#print IsROrC.div_I /-
+#print RCLike.div_I /-
 @[simp, is_R_or_C_simps]
 theorem div_I (z : K) : z / i = -(z * i) := by rw [div_eq_mul_inv, inv_I, mul_neg]
-#align is_R_or_C.div_I IsROrC.div_I
+#align is_R_or_C.div_I RCLike.div_I
 -/
 
-#print IsROrC.normSq_inv /-
+#print RCLike.normSq_inv /-
 @[simp, is_R_or_C_simps]
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ (@normSq K _) z
-#align is_R_or_C.norm_sq_inv IsROrC.normSq_inv
+#align is_R_or_C.norm_sq_inv RCLike.normSq_inv
 -/
 
-#print IsROrC.normSq_div /-
+#print RCLike.normSq_div /-
 @[simp, is_R_or_C_simps]
 theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ (@normSq K _) z w
-#align is_R_or_C.norm_sq_div IsROrC.normSq_div
+#align is_R_or_C.norm_sq_div RCLike.normSq_div
 -/
 
-#print IsROrC.norm_conj /-
+#print RCLike.norm_conj /-
 @[simp, is_R_or_C_simps]
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_norm_sq_eq_norm, norm_sq_conj]
-#align is_R_or_C.norm_conj IsROrC.norm_conj
+#align is_R_or_C.norm_conj RCLike.norm_conj
 -/
 
 instance (priority := 100) : CstarRing K
@@ -813,233 +797,233 @@ instance (priority := 100) : CstarRing K
 /-! ### Cast lemmas -/
 
 
-#print IsROrC.ofReal_natCast /-
+#print RCLike.ofReal_natCast /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_natCast (n : ℕ) : ((n : ℝ) : K) = n :=
   map_natCast (algebraMap ℝ K) n
-#align is_R_or_C.of_real_nat_cast IsROrC.ofReal_natCast
+#align is_R_or_C.of_real_nat_cast RCLike.ofReal_natCast
 -/
 
-#print IsROrC.natCast_re /-
+#print RCLike.natCast_re /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem natCast_re (n : ℕ) : re (n : K) = n := by rw [← of_real_nat_cast, of_real_re]
-#align is_R_or_C.nat_cast_re IsROrC.natCast_re
+#align is_R_or_C.nat_cast_re RCLike.natCast_re
 -/
 
-#print IsROrC.natCast_im /-
+#print RCLike.natCast_im /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem natCast_im (n : ℕ) : im (n : K) = 0 := by rw [← of_real_nat_cast, of_real_im]
-#align is_R_or_C.nat_cast_im IsROrC.natCast_im
+#align is_R_or_C.nat_cast_im RCLike.natCast_im
 -/
 
-#print IsROrC.ofReal_intCast /-
+#print RCLike.ofReal_intCast /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : K) = n :=
   map_intCast (algebraMap ℝ K) n
-#align is_R_or_C.of_real_int_cast IsROrC.ofReal_intCast
+#align is_R_or_C.of_real_int_cast RCLike.ofReal_intCast
 -/
 
-#print IsROrC.intCast_re /-
+#print RCLike.intCast_re /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem intCast_re (n : ℤ) : re (n : K) = n := by rw [← of_real_int_cast, of_real_re]
-#align is_R_or_C.int_cast_re IsROrC.intCast_re
+#align is_R_or_C.int_cast_re RCLike.intCast_re
 -/
 
-#print IsROrC.intCast_im /-
+#print RCLike.intCast_im /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem intCast_im (n : ℤ) : im (n : K) = 0 := by rw [← of_real_int_cast, of_real_im]
-#align is_R_or_C.int_cast_im IsROrC.intCast_im
+#align is_R_or_C.int_cast_im RCLike.intCast_im
 -/
 
-#print IsROrC.ofReal_ratCast /-
+#print RCLike.ofReal_ratCast /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_ratCast (n : ℚ) : ((n : ℝ) : K) = n :=
   map_ratCast (algebraMap ℝ K) n
-#align is_R_or_C.of_real_rat_cast IsROrC.ofReal_ratCast
+#align is_R_or_C.of_real_rat_cast RCLike.ofReal_ratCast
 -/
 
-#print IsROrC.ratCast_re /-
+#print RCLike.ratCast_re /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ratCast_re (q : ℚ) : re (q : K) = q := by rw [← of_real_rat_cast, of_real_re]
-#align is_R_or_C.rat_cast_re IsROrC.ratCast_re
+#align is_R_or_C.rat_cast_re RCLike.ratCast_re
 -/
 
-#print IsROrC.ratCast_im /-
+#print RCLike.ratCast_im /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ratCast_im (q : ℚ) : im (q : K) = 0 := by rw [← of_real_rat_cast, of_real_im]
-#align is_R_or_C.rat_cast_im IsROrC.ratCast_im
+#align is_R_or_C.rat_cast_im RCLike.ratCast_im
 -/
 
 /-! ### Norm -/
 
 
-#print IsROrC.norm_of_nonneg /-
+#print RCLike.norm_of_nonneg /-
 theorem norm_of_nonneg {r : ℝ} (h : 0 ≤ r) : ‖(r : K)‖ = r :=
   (norm_ofReal _).trans (abs_of_nonneg h)
-#align is_R_or_C.norm_of_nonneg IsROrC.norm_of_nonneg
+#align is_R_or_C.norm_of_nonneg RCLike.norm_of_nonneg
 -/
 
-#print IsROrC.norm_natCast /-
+#print RCLike.norm_natCast /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n := by rw [← of_real_nat_cast];
   exact norm_of_nonneg (Nat.cast_nonneg n)
-#align is_R_or_C.norm_nat_cast IsROrC.norm_natCast
+#align is_R_or_C.norm_nat_cast RCLike.norm_natCast
 -/
 
-#print IsROrC.mul_self_norm /-
+#print RCLike.mul_self_norm /-
 theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [norm_sq_eq_def', sq]
-#align is_R_or_C.mul_self_norm IsROrC.mul_self_norm
+#align is_R_or_C.mul_self_norm RCLike.mul_self_norm
 -/
 
 attribute [is_R_or_C_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
 
-#print IsROrC.norm_two /-
+#print RCLike.norm_two /-
 @[simp, is_R_or_C_simps]
 theorem norm_two : ‖(2 : K)‖ = 2 := by rw [← Nat.cast_two, norm_nat_cast, Nat.cast_two]
-#align is_R_or_C.norm_two IsROrC.norm_two
+#align is_R_or_C.norm_two RCLike.norm_two
 -/
 
-#print IsROrC.abs_re_le_norm /-
+#print RCLike.abs_re_le_norm /-
 theorem abs_re_le_norm (z : K) : |re z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (re z)) (norm_nonneg _), abs_mul_abs_self,
       mul_self_norm] <;>
     apply re_sq_le_norm_sq
-#align is_R_or_C.abs_re_le_norm IsROrC.abs_re_le_norm
+#align is_R_or_C.abs_re_le_norm RCLike.abs_re_le_norm
 -/
 
-#print IsROrC.abs_im_le_norm /-
+#print RCLike.abs_im_le_norm /-
 theorem abs_im_le_norm (z : K) : |im z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (im z)) (norm_nonneg _), abs_mul_abs_self,
       mul_self_norm] <;>
     apply im_sq_le_norm_sq
-#align is_R_or_C.abs_im_le_norm IsROrC.abs_im_le_norm
+#align is_R_or_C.abs_im_le_norm RCLike.abs_im_le_norm
 -/
 
-#print IsROrC.norm_re_le_norm /-
+#print RCLike.norm_re_le_norm /-
 theorem norm_re_le_norm (z : K) : ‖re z‖ ≤ ‖z‖ :=
   abs_re_le_norm z
-#align is_R_or_C.norm_re_le_norm IsROrC.norm_re_le_norm
+#align is_R_or_C.norm_re_le_norm RCLike.norm_re_le_norm
 -/
 
-#print IsROrC.norm_im_le_norm /-
+#print RCLike.norm_im_le_norm /-
 theorem norm_im_le_norm (z : K) : ‖im z‖ ≤ ‖z‖ :=
   abs_im_le_norm z
-#align is_R_or_C.norm_im_le_norm IsROrC.norm_im_le_norm
+#align is_R_or_C.norm_im_le_norm RCLike.norm_im_le_norm
 -/
 
-#print IsROrC.re_le_norm /-
+#print RCLike.re_le_norm /-
 theorem re_le_norm (z : K) : re z ≤ ‖z‖ :=
   (abs_le.1 (abs_re_le_norm z)).2
-#align is_R_or_C.re_le_norm IsROrC.re_le_norm
+#align is_R_or_C.re_le_norm RCLike.re_le_norm
 -/
 
-#print IsROrC.im_le_norm /-
+#print RCLike.im_le_norm /-
 theorem im_le_norm (z : K) : im z ≤ ‖z‖ :=
   (abs_le.1 (abs_im_le_norm _)).2
-#align is_R_or_C.im_le_norm IsROrC.im_le_norm
+#align is_R_or_C.im_le_norm RCLike.im_le_norm
 -/
 
-#print IsROrC.im_eq_zero_of_le /-
+#print RCLike.im_eq_zero_of_le /-
 theorem im_eq_zero_of_le {a : K} (h : ‖a‖ ≤ re a) : im a = 0 := by
   simpa only [mul_self_norm a, norm_sq_apply, self_eq_add_right, mul_self_eq_zero] using
     congr_arg (fun z => z * z) ((re_le_norm a).antisymm h)
-#align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_le
+#align is_R_or_C.im_eq_zero_of_le RCLike.im_eq_zero_of_le
 -/
 
-#print IsROrC.re_eq_self_of_le /-
+#print RCLike.re_eq_self_of_le /-
 theorem re_eq_self_of_le {a : K} (h : ‖a‖ ≤ re a) : (re a : K) = a := by
   rw [(is_real_tfae a).out 2 3, im_eq_zero_of_le h]
-#align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_le
+#align is_R_or_C.re_eq_self_of_le RCLike.re_eq_self_of_le
 -/
 
 open IsAbsoluteValue
 
-#print IsROrC.abs_re_div_norm_le_one /-
+#print RCLike.abs_re_div_norm_le_one /-
 theorem abs_re_div_norm_le_one (z : K) : |re z / ‖z‖| ≤ 1 :=
   by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_re_le_norm _) (norm_nonneg _)
-#align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_one
+#align is_R_or_C.abs_re_div_norm_le_one RCLike.abs_re_div_norm_le_one
 -/
 
-#print IsROrC.abs_im_div_norm_le_one /-
+#print RCLike.abs_im_div_norm_le_one /-
 theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
   by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_im_le_norm _) (norm_nonneg _)
-#align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
+#align is_R_or_C.abs_im_div_norm_le_one RCLike.abs_im_div_norm_le_one
 -/
 
-#print IsROrC.norm_I_of_ne_zero /-
+#print RCLike.norm_I_of_ne_zero /-
 theorem norm_I_of_ne_zero (hI : (i : K) ≠ 0) : ‖(i : K)‖ = 1 := by
   rw [← mul_self_inj_of_nonneg (norm_nonneg I) zero_le_one, one_mul, ← norm_mul,
     I_mul_I_of_nonzero hI, norm_neg, norm_one]
-#align is_R_or_C.norm_I_of_ne_zero IsROrC.norm_I_of_ne_zero
+#align is_R_or_C.norm_I_of_ne_zero RCLike.norm_I_of_ne_zero
 -/
 
-#print IsROrC.re_eq_norm_of_mul_conj /-
+#print RCLike.re_eq_norm_of_mul_conj /-
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, of_real_re, norm_of_real, abs_of_nonneg (norm_sq_nonneg _)]
-#align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj
+#align is_R_or_C.re_eq_norm_of_mul_conj RCLike.re_eq_norm_of_mul_conj
 -/
 
-#print IsROrC.norm_sq_re_add_conj /-
+#print RCLike.norm_sq_re_add_conj /-
 theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
   rw [add_conj, norm_mul, norm_two, norm_of_real, two_mul (re x : K), map_add, of_real_re, ←
     two_mul, mul_pow, mul_pow, sq_abs]
-#align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conj
+#align is_R_or_C.norm_sq_re_add_conj RCLike.norm_sq_re_add_conj
 -/
 
-#print IsROrC.norm_sq_re_conj_add /-
+#print RCLike.norm_sq_re_conj_add /-
 theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2 := by
   rw [add_comm, norm_sq_re_add_conj]
-#align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_add
+#align is_R_or_C.norm_sq_re_conj_add RCLike.norm_sq_re_conj_add
 -/
 
 /-! ### Cauchy sequences -/
 
 
-#print IsROrC.isCauSeq_re /-
+#print RCLike.isCauSeq_re /-
 theorem isCauSeq_re (f : CauSeq K norm) : IsCauSeq abs fun n => re (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_re_le_norm (f j - f i)) (H _ ij)
-#align is_R_or_C.is_cau_seq_re IsROrC.isCauSeq_re
+#align is_R_or_C.is_cau_seq_re RCLike.isCauSeq_re
 -/
 
-#print IsROrC.isCauSeq_im /-
+#print RCLike.isCauSeq_im /-
 theorem isCauSeq_im (f : CauSeq K norm) : IsCauSeq abs fun n => im (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_im_le_norm (f j - f i)) (H _ ij)
-#align is_R_or_C.is_cau_seq_im IsROrC.isCauSeq_im
+#align is_R_or_C.is_cau_seq_im RCLike.isCauSeq_im
 -/
 
-#print IsROrC.cauSeqRe /-
+#print RCLike.cauSeqRe /-
 /-- The real part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_re f⟩
-#align is_R_or_C.cau_seq_re IsROrC.cauSeqRe
+#align is_R_or_C.cau_seq_re RCLike.cauSeqRe
 -/
 
-#print IsROrC.cauSeqIm /-
+#print RCLike.cauSeqIm /-
 /-- The imaginary part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_im f⟩
-#align is_R_or_C.cau_seq_im IsROrC.cauSeqIm
+#align is_R_or_C.cau_seq_im RCLike.cauSeqIm
 -/
 
-#print IsROrC.isCauSeq_norm /-
+#print RCLike.isCauSeq_norm /-
 theorem isCauSeq_norm {f : ℕ → K} (hf : IsCauSeq norm f) : IsCauSeq abs (norm ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
   ⟨i, fun j hj => lt_of_le_of_lt (abs_norm_sub_norm_le _ _) (hi j hj)⟩
-#align is_R_or_C.is_cau_seq_norm IsROrC.isCauSeq_norm
+#align is_R_or_C.is_cau_seq_norm RCLike.isCauSeq_norm
 -/
 
-end IsROrC
+end RCLike
 
 section Instances
 
-#print Real.isROrC /-
-noncomputable instance Real.isROrC : IsROrC ℝ :=
+#print Real.RCLike /-
+noncomputable instance Real.RCLike : RCLike ℝ :=
   { Real.denselyNormedField,
     Real.metricSpace with
     re := AddMonoidHom.id ℝ
@@ -1063,155 +1047,155 @@ noncomputable instance Real.isROrC : IsROrC ℝ :=
       simp only [sq, Real.norm_eq_abs, ← abs_mul, abs_mul_self z, add_zero, MulZeroClass.mul_zero,
         AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
     hMul_im_i_ax := fun z => by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply] }
-#align real.is_R_or_C Real.isROrC
+#align real.is_R_or_C Real.RCLike
 -/
 
 end Instances
 
-namespace IsROrC
+namespace RCLike
 
 open scoped ComplexConjugate
 
 section CleanupLemmas
 
-local notation "reR" => @IsROrC.re ℝ _
+local notation "reR" => @RCLike.re ℝ _
 
-local notation "imR" => @IsROrC.im ℝ _
+local notation "imR" => @RCLike.im ℝ _
 
-local notation "IR" => @IsROrC.i ℝ _
+local notation "IR" => @RCLike.i ℝ _
 
-local notation "norm_sqR" => @IsROrC.normSq ℝ _
+local notation "norm_sqR" => @RCLike.normSq ℝ _
 
-#print IsROrC.re_to_real /-
+#print RCLike.re_to_real /-
 @[simp, is_R_or_C_simps]
 theorem re_to_real {x : ℝ} : reR x = x :=
   rfl
-#align is_R_or_C.re_to_real IsROrC.re_to_real
+#align is_R_or_C.re_to_real RCLike.re_to_real
 -/
 
-#print IsROrC.im_to_real /-
+#print RCLike.im_to_real /-
 @[simp, is_R_or_C_simps]
 theorem im_to_real {x : ℝ} : imR x = 0 :=
   rfl
-#align is_R_or_C.im_to_real IsROrC.im_to_real
+#align is_R_or_C.im_to_real RCLike.im_to_real
 -/
 
-#print IsROrC.conj_to_real /-
+#print RCLike.conj_to_real /-
 @[simp, is_R_or_C_simps]
 theorem conj_to_real {x : ℝ} : conj x = x :=
   rfl
-#align is_R_or_C.conj_to_real IsROrC.conj_to_real
+#align is_R_or_C.conj_to_real RCLike.conj_to_real
 -/
 
-#print IsROrC.I_to_real /-
+#print RCLike.I_to_real /-
 @[simp, is_R_or_C_simps]
 theorem I_to_real : IR = 0 :=
   rfl
-#align is_R_or_C.I_to_real IsROrC.I_to_real
+#align is_R_or_C.I_to_real RCLike.I_to_real
 -/
 
-#print IsROrC.normSq_to_real /-
+#print RCLike.normSq_to_real /-
 @[simp, is_R_or_C_simps]
-theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [IsROrC.normSq]
-#align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_real
+theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [RCLike.normSq]
+#align is_R_or_C.norm_sq_to_real RCLike.normSq_to_real
 -/
 
-#print IsROrC.ofReal_real_eq_id /-
+#print RCLike.ofReal_real_eq_id /-
 @[simp]
 theorem ofReal_real_eq_id : @coe ℝ ℝ _ = id :=
   rfl
-#align is_R_or_C.coe_real_eq_id IsROrC.ofReal_real_eq_id
+#align is_R_or_C.coe_real_eq_id RCLike.ofReal_real_eq_id
 -/
 
 end CleanupLemmas
 
 section LinearMaps
 
-#print IsROrC.reLm /-
+#print RCLike.reLm /-
 /-- The real part in a `is_R_or_C` field, as a linear map. -/
 def reLm : K →ₗ[ℝ] ℝ :=
   { re with map_smul' := smul_re }
-#align is_R_or_C.re_lm IsROrC.reLm
+#align is_R_or_C.re_lm RCLike.reLm
 -/
 
-#print IsROrC.reLm_coe /-
+#print RCLike.reLm_coe /-
 @[simp, is_R_or_C_simps]
 theorem reLm_coe : (reLm : K → ℝ) = re :=
   rfl
-#align is_R_or_C.re_lm_coe IsROrC.reLm_coe
+#align is_R_or_C.re_lm_coe RCLike.reLm_coe
 -/
 
-#print IsROrC.reCLM /-
+#print RCLike.reCLM /-
 /-- The real part in a `is_R_or_C` field, as a continuous linear map. -/
 noncomputable def reCLM : K →L[ℝ] ℝ :=
   LinearMap.mkContinuous reLm 1 fun x => by rw [one_mul]; exact abs_re_le_norm x
-#align is_R_or_C.re_clm IsROrC.reCLM
+#align is_R_or_C.re_clm RCLike.reCLM
 -/
 
-#print IsROrC.reCLM_coe /-
+#print RCLike.reCLM_coe /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem reCLM_coe : ((reCLM : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
   rfl
-#align is_R_or_C.re_clm_coe IsROrC.reCLM_coe
+#align is_R_or_C.re_clm_coe RCLike.reCLM_coe
 -/
 
-#print IsROrC.reCLM_apply /-
+#print RCLike.reCLM_apply /-
 @[simp, is_R_or_C_simps]
 theorem reCLM_apply : ((reCLM : K →L[ℝ] ℝ) : K → ℝ) = re :=
   rfl
-#align is_R_or_C.re_clm_apply IsROrC.reCLM_apply
+#align is_R_or_C.re_clm_apply RCLike.reCLM_apply
 -/
 
-#print IsROrC.continuous_re /-
+#print RCLike.continuous_re /-
 @[continuity]
 theorem continuous_re : Continuous (re : K → ℝ) :=
   reCLM.Continuous
-#align is_R_or_C.continuous_re IsROrC.continuous_re
+#align is_R_or_C.continuous_re RCLike.continuous_re
 -/
 
-#print IsROrC.imLm /-
+#print RCLike.imLm /-
 /-- The imaginary part in a `is_R_or_C` field, as a linear map. -/
 def imLm : K →ₗ[ℝ] ℝ :=
   { im with map_smul' := smul_im }
-#align is_R_or_C.im_lm IsROrC.imLm
+#align is_R_or_C.im_lm RCLike.imLm
 -/
 
-#print IsROrC.imLm_coe /-
+#print RCLike.imLm_coe /-
 @[simp, is_R_or_C_simps]
 theorem imLm_coe : (imLm : K → ℝ) = im :=
   rfl
-#align is_R_or_C.im_lm_coe IsROrC.imLm_coe
+#align is_R_or_C.im_lm_coe RCLike.imLm_coe
 -/
 
-#print IsROrC.imCLM /-
+#print RCLike.imCLM /-
 /-- The imaginary part in a `is_R_or_C` field, as a continuous linear map. -/
 noncomputable def imCLM : K →L[ℝ] ℝ :=
   LinearMap.mkContinuous imLm 1 fun x => by rw [one_mul]; exact abs_im_le_norm x
-#align is_R_or_C.im_clm IsROrC.imCLM
+#align is_R_or_C.im_clm RCLike.imCLM
 -/
 
-#print IsROrC.imCLM_coe /-
+#print RCLike.imCLM_coe /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem imCLM_coe : ((imCLM : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
   rfl
-#align is_R_or_C.im_clm_coe IsROrC.imCLM_coe
+#align is_R_or_C.im_clm_coe RCLike.imCLM_coe
 -/
 
-#print IsROrC.imCLM_apply /-
+#print RCLike.imCLM_apply /-
 @[simp, is_R_or_C_simps]
 theorem imCLM_apply : ((imCLM : K →L[ℝ] ℝ) : K → ℝ) = im :=
   rfl
-#align is_R_or_C.im_clm_apply IsROrC.imCLM_apply
+#align is_R_or_C.im_clm_apply RCLike.imCLM_apply
 -/
 
-#print IsROrC.continuous_im /-
+#print RCLike.continuous_im /-
 @[continuity]
 theorem continuous_im : Continuous (im : K → ℝ) :=
   imCLM.Continuous
-#align is_R_or_C.continuous_im IsROrC.continuous_im
+#align is_R_or_C.continuous_im RCLike.continuous_im
 -/
 
-#print IsROrC.conjAe /-
+#print RCLike.conjAe /-
 /-- Conjugate as an `ℝ`-algebra equivalence -/
 def conjAe : K ≃ₐ[ℝ] K :=
   { conj with
@@ -1219,127 +1203,127 @@ def conjAe : K ≃ₐ[ℝ] K :=
     left_inv := conj_conj
     right_inv := conj_conj
     commutes' := conj_ofReal }
-#align is_R_or_C.conj_ae IsROrC.conjAe
+#align is_R_or_C.conj_ae RCLike.conjAe
 -/
 
-#print IsROrC.conjAe_coe /-
+#print RCLike.conjAe_coe /-
 @[simp, is_R_or_C_simps]
 theorem conjAe_coe : (conjAe : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_ae_coe IsROrC.conjAe_coe
+#align is_R_or_C.conj_ae_coe RCLike.conjAe_coe
 -/
 
-#print IsROrC.conjLIE /-
+#print RCLike.conjLIE /-
 /-- Conjugate as a linear isometry -/
 noncomputable def conjLIE : K ≃ₗᵢ[ℝ] K :=
   ⟨conjAe.toLinearEquiv, fun _ => norm_conj⟩
-#align is_R_or_C.conj_lie IsROrC.conjLIE
+#align is_R_or_C.conj_lie RCLike.conjLIE
 -/
 
-#print IsROrC.conjLIE_apply /-
+#print RCLike.conjLIE_apply /-
 @[simp, is_R_or_C_simps]
 theorem conjLIE_apply : (conjLIE : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_lie_apply IsROrC.conjLIE_apply
+#align is_R_or_C.conj_lie_apply RCLike.conjLIE_apply
 -/
 
-#print IsROrC.conjCLE /-
+#print RCLike.conjCLE /-
 /-- Conjugate as a continuous linear equivalence -/
 noncomputable def conjCLE : K ≃L[ℝ] K :=
   @conjLIE K _
-#align is_R_or_C.conj_cle IsROrC.conjCLE
+#align is_R_or_C.conj_cle RCLike.conjCLE
 -/
 
-#print IsROrC.conjCLE_coe /-
+#print RCLike.conjCLE_coe /-
 @[simp, is_R_or_C_simps]
 theorem conjCLE_coe : (@conjCLE K _).toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
-#align is_R_or_C.conj_cle_coe IsROrC.conjCLE_coe
+#align is_R_or_C.conj_cle_coe RCLike.conjCLE_coe
 -/
 
-#print IsROrC.conjCLE_apply /-
+#print RCLike.conjCLE_apply /-
 @[simp, is_R_or_C_simps]
 theorem conjCLE_apply : (conjCLE : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_cle_apply IsROrC.conjCLE_apply
+#align is_R_or_C.conj_cle_apply RCLike.conjCLE_apply
 -/
 
 instance (priority := 100) : ContinuousStar K :=
   ⟨conjLIE.Continuous⟩
 
-#print IsROrC.continuous_conj /-
+#print RCLike.continuous_conj /-
 @[continuity]
 theorem continuous_conj : Continuous (conj : K → K) :=
   continuous_star
-#align is_R_or_C.continuous_conj IsROrC.continuous_conj
+#align is_R_or_C.continuous_conj RCLike.continuous_conj
 -/
 
-#print IsROrC.ofRealAm /-
+#print RCLike.ofRealAm /-
 /-- The `ℝ → K` coercion, as a linear map -/
 noncomputable def ofRealAm : ℝ →ₐ[ℝ] K :=
   Algebra.ofId ℝ K
-#align is_R_or_C.of_real_am IsROrC.ofRealAm
+#align is_R_or_C.of_real_am RCLike.ofRealAm
 -/
 
-#print IsROrC.ofRealAm_coe /-
+#print RCLike.ofRealAm_coe /-
 @[simp, is_R_or_C_simps]
 theorem ofRealAm_coe : (ofRealAm : ℝ → K) = coe :=
   rfl
-#align is_R_or_C.of_real_am_coe IsROrC.ofRealAm_coe
+#align is_R_or_C.of_real_am_coe RCLike.ofRealAm_coe
 -/
 
-#print IsROrC.ofRealLI /-
+#print RCLike.ofRealLI /-
 /-- The ℝ → K coercion, as a linear isometry -/
 noncomputable def ofRealLI : ℝ →ₗᵢ[ℝ] K
     where
   toLinearMap := ofRealAm.toLinearMap
   norm_map' := norm_ofReal
-#align is_R_or_C.of_real_li IsROrC.ofRealLI
+#align is_R_or_C.of_real_li RCLike.ofRealLI
 -/
 
-#print IsROrC.ofRealLI_apply /-
+#print RCLike.ofRealLI_apply /-
 @[simp, is_R_or_C_simps]
 theorem ofRealLI_apply : (ofRealLI : ℝ → K) = coe :=
   rfl
-#align is_R_or_C.of_real_li_apply IsROrC.ofRealLI_apply
+#align is_R_or_C.of_real_li_apply RCLike.ofRealLI_apply
 -/
 
-#print IsROrC.ofRealCLM /-
+#print RCLike.ofRealCLM /-
 /-- The `ℝ → K` coercion, as a continuous linear map -/
 noncomputable def ofRealCLM : ℝ →L[ℝ] K :=
   ofRealLI.toContinuousLinearMap
-#align is_R_or_C.of_real_clm IsROrC.ofRealCLM
+#align is_R_or_C.of_real_clm RCLike.ofRealCLM
 -/
 
-#print IsROrC.ofRealCLM_coe /-
+#print RCLike.ofRealCLM_coe /-
 @[simp, is_R_or_C_simps]
 theorem ofRealCLM_coe : (@ofRealCLM K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinearMap :=
   rfl
-#align is_R_or_C.of_real_clm_coe IsROrC.ofRealCLM_coe
+#align is_R_or_C.of_real_clm_coe RCLike.ofRealCLM_coe
 -/
 
-#print IsROrC.ofRealCLM_apply /-
+#print RCLike.ofRealCLM_apply /-
 @[simp, is_R_or_C_simps]
 theorem ofRealCLM_apply : (ofRealCLM : ℝ → K) = coe :=
   rfl
-#align is_R_or_C.of_real_clm_apply IsROrC.ofRealCLM_apply
+#align is_R_or_C.of_real_clm_apply RCLike.ofRealCLM_apply
 -/
 
-#print IsROrC.continuous_ofReal /-
+#print RCLike.continuous_ofReal /-
 @[continuity]
 theorem continuous_ofReal : Continuous (coe : ℝ → K) :=
   ofRealLI.Continuous
-#align is_R_or_C.continuous_of_real IsROrC.continuous_ofReal
+#align is_R_or_C.continuous_of_real RCLike.continuous_ofReal
 -/
 
-#print IsROrC.continuous_normSq /-
+#print RCLike.continuous_normSq /-
 @[continuity]
 theorem continuous_normSq : Continuous (normSq : K → ℝ) :=
   (continuous_re.mul continuous_re).add (continuous_im.mul continuous_im)
-#align is_R_or_C.continuous_norm_sq IsROrC.continuous_normSq
+#align is_R_or_C.continuous_norm_sq RCLike.continuous_normSq
 -/
 
 end LinearMaps
 
-end IsROrC
+end RCLike
 

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

@@ -1141,31 +1141,31 @@ theorem reLm_coe : (reLm : K → ℝ) = re :=
 #align is_R_or_C.re_lm_coe IsROrC.reLm_coe
 -/
 
-#print IsROrC.reClm /-
+#print IsROrC.reCLM /-
 /-- The real part in a `is_R_or_C` field, as a continuous linear map. -/
-noncomputable def reClm : K →L[ℝ] ℝ :=
+noncomputable def reCLM : K →L[ℝ] ℝ :=
   LinearMap.mkContinuous reLm 1 fun x => by rw [one_mul]; exact abs_re_le_norm x
-#align is_R_or_C.re_clm IsROrC.reClm
+#align is_R_or_C.re_clm IsROrC.reCLM
 -/
 
-#print IsROrC.reClm_coe /-
+#print IsROrC.reCLM_coe /-
 @[simp, is_R_or_C_simps, norm_cast]
-theorem reClm_coe : ((reClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
+theorem reCLM_coe : ((reCLM : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
   rfl
-#align is_R_or_C.re_clm_coe IsROrC.reClm_coe
+#align is_R_or_C.re_clm_coe IsROrC.reCLM_coe
 -/
 
-#print IsROrC.reClm_apply /-
+#print IsROrC.reCLM_apply /-
 @[simp, is_R_or_C_simps]
-theorem reClm_apply : ((reClm : K →L[ℝ] ℝ) : K → ℝ) = re :=
+theorem reCLM_apply : ((reCLM : K →L[ℝ] ℝ) : K → ℝ) = re :=
   rfl
-#align is_R_or_C.re_clm_apply IsROrC.reClm_apply
+#align is_R_or_C.re_clm_apply IsROrC.reCLM_apply
 -/
 
 #print IsROrC.continuous_re /-
 @[continuity]
 theorem continuous_re : Continuous (re : K → ℝ) :=
-  reClm.Continuous
+  reCLM.Continuous
 #align is_R_or_C.continuous_re IsROrC.continuous_re
 -/
 
@@ -1183,31 +1183,31 @@ theorem imLm_coe : (imLm : K → ℝ) = im :=
 #align is_R_or_C.im_lm_coe IsROrC.imLm_coe
 -/
 
-#print IsROrC.imClm /-
+#print IsROrC.imCLM /-
 /-- The imaginary part in a `is_R_or_C` field, as a continuous linear map. -/
-noncomputable def imClm : K →L[ℝ] ℝ :=
+noncomputable def imCLM : K →L[ℝ] ℝ :=
   LinearMap.mkContinuous imLm 1 fun x => by rw [one_mul]; exact abs_im_le_norm x
-#align is_R_or_C.im_clm IsROrC.imClm
+#align is_R_or_C.im_clm IsROrC.imCLM
 -/
 
-#print IsROrC.imClm_coe /-
+#print IsROrC.imCLM_coe /-
 @[simp, is_R_or_C_simps, norm_cast]
-theorem imClm_coe : ((imClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
+theorem imCLM_coe : ((imCLM : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
   rfl
-#align is_R_or_C.im_clm_coe IsROrC.imClm_coe
+#align is_R_or_C.im_clm_coe IsROrC.imCLM_coe
 -/
 
-#print IsROrC.imClm_apply /-
+#print IsROrC.imCLM_apply /-
 @[simp, is_R_or_C_simps]
-theorem imClm_apply : ((imClm : K →L[ℝ] ℝ) : K → ℝ) = im :=
+theorem imCLM_apply : ((imCLM : K →L[ℝ] ℝ) : K → ℝ) = im :=
   rfl
-#align is_R_or_C.im_clm_apply IsROrC.imClm_apply
+#align is_R_or_C.im_clm_apply IsROrC.imCLM_apply
 -/
 
 #print IsROrC.continuous_im /-
 @[continuity]
 theorem continuous_im : Continuous (im : K → ℝ) :=
-  imClm.Continuous
+  imCLM.Continuous
 #align is_R_or_C.continuous_im IsROrC.continuous_im
 -/
 
@@ -1229,43 +1229,43 @@ theorem conjAe_coe : (conjAe : K → K) = conj :=
 #align is_R_or_C.conj_ae_coe IsROrC.conjAe_coe
 -/
 
-#print IsROrC.conjLie /-
+#print IsROrC.conjLIE /-
 /-- Conjugate as a linear isometry -/
-noncomputable def conjLie : K ≃ₗᵢ[ℝ] K :=
+noncomputable def conjLIE : K ≃ₗᵢ[ℝ] K :=
   ⟨conjAe.toLinearEquiv, fun _ => norm_conj⟩
-#align is_R_or_C.conj_lie IsROrC.conjLie
+#align is_R_or_C.conj_lie IsROrC.conjLIE
 -/
 
-#print IsROrC.conjLie_apply /-
+#print IsROrC.conjLIE_apply /-
 @[simp, is_R_or_C_simps]
-theorem conjLie_apply : (conjLie : K → K) = conj :=
+theorem conjLIE_apply : (conjLIE : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_lie_apply IsROrC.conjLie_apply
+#align is_R_or_C.conj_lie_apply IsROrC.conjLIE_apply
 -/
 
-#print IsROrC.conjCle /-
+#print IsROrC.conjCLE /-
 /-- Conjugate as a continuous linear equivalence -/
-noncomputable def conjCle : K ≃L[ℝ] K :=
-  @conjLie K _
-#align is_R_or_C.conj_cle IsROrC.conjCle
+noncomputable def conjCLE : K ≃L[ℝ] K :=
+  @conjLIE K _
+#align is_R_or_C.conj_cle IsROrC.conjCLE
 -/
 
-#print IsROrC.conjCle_coe /-
+#print IsROrC.conjCLE_coe /-
 @[simp, is_R_or_C_simps]
-theorem conjCle_coe : (@conjCle K _).toLinearEquiv = conjAe.toLinearEquiv :=
+theorem conjCLE_coe : (@conjCLE K _).toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
-#align is_R_or_C.conj_cle_coe IsROrC.conjCle_coe
+#align is_R_or_C.conj_cle_coe IsROrC.conjCLE_coe
 -/
 
-#print IsROrC.conjCle_apply /-
+#print IsROrC.conjCLE_apply /-
 @[simp, is_R_or_C_simps]
-theorem conjCle_apply : (conjCle : K → K) = conj :=
+theorem conjCLE_apply : (conjCLE : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_cle_apply IsROrC.conjCle_apply
+#align is_R_or_C.conj_cle_apply IsROrC.conjCLE_apply
 -/
 
 instance (priority := 100) : ContinuousStar K :=
-  ⟨conjLie.Continuous⟩
+  ⟨conjLIE.Continuous⟩
 
 #print IsROrC.continuous_conj /-
 @[continuity]
@@ -1288,47 +1288,47 @@ theorem ofRealAm_coe : (ofRealAm : ℝ → K) = coe :=
 #align is_R_or_C.of_real_am_coe IsROrC.ofRealAm_coe
 -/
 
-#print IsROrC.ofRealLi /-
+#print IsROrC.ofRealLI /-
 /-- The ℝ → K coercion, as a linear isometry -/
-noncomputable def ofRealLi : ℝ →ₗᵢ[ℝ] K
+noncomputable def ofRealLI : ℝ →ₗᵢ[ℝ] K
     where
   toLinearMap := ofRealAm.toLinearMap
   norm_map' := norm_ofReal
-#align is_R_or_C.of_real_li IsROrC.ofRealLi
+#align is_R_or_C.of_real_li IsROrC.ofRealLI
 -/
 
-#print IsROrC.ofRealLi_apply /-
+#print IsROrC.ofRealLI_apply /-
 @[simp, is_R_or_C_simps]
-theorem ofRealLi_apply : (ofRealLi : ℝ → K) = coe :=
+theorem ofRealLI_apply : (ofRealLI : ℝ → K) = coe :=
   rfl
-#align is_R_or_C.of_real_li_apply IsROrC.ofRealLi_apply
+#align is_R_or_C.of_real_li_apply IsROrC.ofRealLI_apply
 -/
 
-#print IsROrC.ofRealClm /-
+#print IsROrC.ofRealCLM /-
 /-- The `ℝ → K` coercion, as a continuous linear map -/
-noncomputable def ofRealClm : ℝ →L[ℝ] K :=
-  ofRealLi.toContinuousLinearMap
-#align is_R_or_C.of_real_clm IsROrC.ofRealClm
+noncomputable def ofRealCLM : ℝ →L[ℝ] K :=
+  ofRealLI.toContinuousLinearMap
+#align is_R_or_C.of_real_clm IsROrC.ofRealCLM
 -/
 
-#print IsROrC.ofRealClm_coe /-
+#print IsROrC.ofRealCLM_coe /-
 @[simp, is_R_or_C_simps]
-theorem ofRealClm_coe : (@ofRealClm K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinearMap :=
+theorem ofRealCLM_coe : (@ofRealCLM K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinearMap :=
   rfl
-#align is_R_or_C.of_real_clm_coe IsROrC.ofRealClm_coe
+#align is_R_or_C.of_real_clm_coe IsROrC.ofRealCLM_coe
 -/
 
-#print IsROrC.ofRealClm_apply /-
+#print IsROrC.ofRealCLM_apply /-
 @[simp, is_R_or_C_simps]
-theorem ofRealClm_apply : (ofRealClm : ℝ → K) = coe :=
+theorem ofRealCLM_apply : (ofRealCLM : ℝ → K) = coe :=
   rfl
-#align is_R_or_C.of_real_clm_apply IsROrC.ofRealClm_apply
+#align is_R_or_C.of_real_clm_apply IsROrC.ofRealCLM_apply
 -/
 
 #print IsROrC.continuous_ofReal /-
 @[continuity]
 theorem continuous_ofReal : Continuous (coe : ℝ → K) :=
-  ofRealLi.Continuous
+  ofRealLI.Continuous
 #align is_R_or_C.continuous_of_real IsROrC.continuous_ofReal
 -/
 

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

@@ -336,18 +336,18 @@ theorem real_smul_ofReal (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
 #align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofReal
 -/
 
-#print IsROrC.ofReal_mul_re /-
+#print IsROrC.re_ofReal_mul /-
 @[is_R_or_C_simps]
-theorem ofReal_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
+theorem re_ofReal_mul (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
   simp only [mul_re, of_real_im, MulZeroClass.zero_mul, of_real_re, sub_zero]
-#align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_re
+#align is_R_or_C.of_real_mul_re IsROrC.re_ofReal_mul
 -/
 
-#print IsROrC.ofReal_mul_im /-
+#print IsROrC.im_ofReal_mul /-
 @[is_R_or_C_simps]
-theorem ofReal_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
+theorem im_ofReal_mul (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
   simp only [add_zero, of_real_im, MulZeroClass.zero_mul, of_real_re, mul_im]
-#align is_R_or_C.of_real_mul_im IsROrC.ofReal_mul_im
+#align is_R_or_C.of_real_mul_im IsROrC.im_ofReal_mul
 -/
 
 #print IsROrC.smul_re /-

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

@@ -609,7 +609,7 @@ theorem normSq_one : normSq (1 : K) = 1 :=
 
 #print IsROrC.normSq_nonneg /-
 theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
-  add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
+  add_nonneg (hMul_self_nonneg _) (hMul_self_nonneg _)
 #align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonneg
 -/
 
@@ -654,13 +654,13 @@ theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z
 
 #print IsROrC.re_sq_le_normSq /-
 theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
-  le_add_of_nonneg_right (mul_self_nonneg _)
+  le_add_of_nonneg_right (hMul_self_nonneg _)
 #align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSq
 -/
 
 #print IsROrC.im_sq_le_normSq /-
 theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
-  le_add_of_nonneg_left (mul_self_nonneg _)
+  le_add_of_nonneg_left (hMul_self_nonneg _)
 #align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 -/
-import Mathbin.Data.Real.Sqrt
-import Mathbin.Analysis.NormedSpace.Star.Basic
-import Mathbin.Analysis.NormedSpace.ContinuousLinearMap
+import Data.Real.Sqrt
+import Analysis.NormedSpace.Star.Basic
+import Analysis.NormedSpace.ContinuousLinearMap
 
 #align_import data.is_R_or_C.basic from "leanprover-community/mathlib"@"baa88307f3e699fa7054ef04ec79fa4f056169cb"
 

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

@@ -62,17 +62,17 @@ class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebr
   i : K
   -- Meant to be set to 0 for K=ℝ
   i_re_ax : re I = 0
-  i_mul_i_ax : I = 0 ∨ I * I = -1
+  i_hMul_i_ax : I = 0 ∨ I * I = -1
   re_add_im_ax : ∀ z : K, 𝓚 (re z) + 𝓚 (im z) * I = z
   of_real_re_ax : ∀ r : ℝ, re (𝓚 r) = r
   of_real_im_ax : ∀ r : ℝ, im (𝓚 r) = 0
-  mul_re_ax : ∀ z w : K, re (z * w) = re z * re w - im z * im w
-  mul_im_ax : ∀ z w : K, im (z * w) = re z * im w + im z * re w
+  hMul_re_ax : ∀ z w : K, re (z * w) = re z * re w - im z * im w
+  hMul_im_ax : ∀ z w : K, im (z * w) = re z * im w + im z * re w
   conj_re_ax : ∀ z : K, re (conj z) = re z
   conj_im_ax : ∀ z : K, im (conj z) = -im z
   conj_i_ax : conj I = -I
   norm_sq_eq_def_ax : ∀ z : K, ‖z‖ ^ 2 = re z * re z + im z * im z
-  mul_im_i_ax : ∀ z : K, im z * im I = im z
+  hMul_im_i_ax : ∀ z : K, im z * im I = im z
 #align is_R_or_C IsROrC
 -/
 
@@ -140,14 +140,14 @@ theorem ofReal_im : ∀ r : ℝ, im (r : K) = 0 :=
 #print IsROrC.mul_re /-
 @[simp, is_R_or_C_simps]
 theorem mul_re : ∀ z w : K, re (z * w) = re z * re w - im z * im w :=
-  IsROrC.mul_re_ax
+  IsROrC.hMul_re_ax
 #align is_R_or_C.mul_re IsROrC.mul_re
 -/
 
 #print IsROrC.mul_im /-
 @[simp, is_R_or_C_simps]
 theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
-  IsROrC.mul_im_ax
+  IsROrC.hMul_im_ax
 #align is_R_or_C.mul_im IsROrC.mul_im
 -/
 
@@ -396,7 +396,7 @@ theorem I_re : re (i : K) = 0 :=
 #print IsROrC.I_im /-
 @[simp, is_R_or_C_simps]
 theorem I_im (z : K) : im z * im (i : K) = im z :=
-  mul_im_i_ax z
+  hMul_im_i_ax z
 #align is_R_or_C.I_im IsROrC.I_im
 -/
 
@@ -415,7 +415,7 @@ theorem I_mul_re (z : K) : re (i * z) = -im z := by
 
 #print IsROrC.I_mul_I /-
 theorem I_mul_I : (i : K) = 0 ∨ (i : K) * i = -1 :=
-  i_mul_i_ax
+  i_hMul_i_ax
 #align is_R_or_C.I_mul_I IsROrC.I_mul_I
 -/
 
@@ -642,7 +642,7 @@ theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
 #print IsROrC.normSq_mul /-
 @[simp, is_R_or_C_simps]
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
-  normSq.map_mul z w
+  normSq.map_hMul z w
 #align is_R_or_C.norm_sq_mul IsROrC.normSq_mul
 -/
 
@@ -768,7 +768,7 @@ theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : K) = r ^ n :=
 
 #print IsROrC.I_mul_I_of_nonzero /-
 theorem I_mul_I_of_nonzero : (i : K) ≠ 0 → (i : K) * i = -1 :=
-  i_mul_i_ax.resolve_left
+  i_hMul_i_ax.resolve_left
 #align is_R_or_C.I_mul_I_of_nonzero IsROrC.I_mul_I_of_nonzero
 -/
 
@@ -808,7 +808,7 @@ theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_nor
 -/
 
 instance (priority := 100) : CstarRing K
-    where norm_star_mul_self x := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) norm_conj
+    where norm_star_hMul_self x := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) norm_conj
 
 /-! ### Cast lemmas -/
 
@@ -1046,15 +1046,15 @@ noncomputable instance Real.isROrC : IsROrC ℝ :=
     im := 0
     i := 0
     i_re_ax := by simp only [AddMonoidHom.map_zero]
-    i_mul_i_ax := Or.intro_left _ rfl
+    i_hMul_i_ax := Or.intro_left _ rfl
     re_add_im_ax := fun z => by
       simp only [add_zero, MulZeroClass.mul_zero, Algebra.id.map_eq_id, RingHom.id_apply,
         AddMonoidHom.id_apply]
     of_real_re_ax := fun r => by simp only [AddMonoidHom.id_apply, Algebra.id.map_eq_self]
     of_real_im_ax := fun r => by simp only [AddMonoidHom.zero_apply]
-    mul_re_ax := fun z w => by
+    hMul_re_ax := fun z w => by
       simp only [sub_zero, MulZeroClass.mul_zero, AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
-    mul_im_ax := fun z w => by
+    hMul_im_ax := fun z w => by
       simp only [add_zero, MulZeroClass.zero_mul, MulZeroClass.mul_zero, AddMonoidHom.zero_apply]
     conj_re_ax := fun z => by simp only [starRingEnd_apply, star_id_of_comm]
     conj_im_ax := fun z => by simp only [neg_zero, AddMonoidHom.zero_apply]
@@ -1062,7 +1062,7 @@ noncomputable instance Real.isROrC : IsROrC ℝ :=
     norm_sq_eq_def_ax := fun z => by
       simp only [sq, Real.norm_eq_abs, ← abs_mul, abs_mul_self z, add_zero, MulZeroClass.mul_zero,
         AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
-    mul_im_i_ax := fun z => by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply] }
+    hMul_im_i_ax := fun z => by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply] }
 #align real.is_R_or_C Real.isROrC
 -/
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
-
-! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit baa88307f3e699fa7054ef04ec79fa4f056169cb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Real.Sqrt
 import Mathbin.Analysis.NormedSpace.Star.Basic
 import Mathbin.Analysis.NormedSpace.ContinuousLinearMap
 
+#align_import data.is_R_or_C.basic from "leanprover-community/mathlib"@"baa88307f3e699fa7054ef04ec79fa4f056169cb"
+
 /-!
 # `is_R_or_C`: a typeclass for ℝ or ℂ
 

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

@@ -973,10 +973,12 @@ theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
 #align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
 -/
 
-theorem norm_i_of_ne_zero (hI : (i : K) ≠ 0) : ‖(i : K)‖ = 1 := by
+#print IsROrC.norm_I_of_ne_zero /-
+theorem norm_I_of_ne_zero (hI : (i : K) ≠ 0) : ‖(i : K)‖ = 1 := by
   rw [← mul_self_inj_of_nonneg (norm_nonneg I) zero_le_one, one_mul, ← norm_mul,
     I_mul_I_of_nonzero hI, norm_neg, norm_one]
-#align is_R_or_C.norm_I_of_ne_zero IsROrC.norm_i_of_ne_zero
+#align is_R_or_C.norm_I_of_ne_zero IsROrC.norm_I_of_ne_zero
+-/
 
 #print IsROrC.re_eq_norm_of_mul_conj /-
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/d608fc5d4e69d4cc21885913fb573a88b0deb521

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit 48fb5b5280e7c81672afc9524185ae994553ebf4
+! leanprover-community/mathlib commit baa88307f3e699fa7054ef04ec79fa4f056169cb
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -973,6 +973,11 @@ theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
 #align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
 -/
 
+theorem norm_i_of_ne_zero (hI : (i : K) ≠ 0) : ‖(i : K)‖ = 1 := by
+  rw [← mul_self_inj_of_nonneg (norm_nonneg I) zero_le_one, one_mul, ← norm_mul,
+    I_mul_I_of_nonzero hI, norm_neg, norm_one]
+#align is_R_or_C.norm_I_of_ne_zero IsROrC.norm_i_of_ne_zero
+
 #print IsROrC.re_eq_norm_of_mul_conj /-
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, of_real_re, norm_of_real, abs_of_nonneg (norm_sq_nonneg _)]

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit 6cf5900728239efa287df7761ec2a1ac9cf39b29
+! leanprover-community/mathlib commit 48fb5b5280e7c81672afc9524185ae994553ebf4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -81,10 +81,6 @@ class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebr
 
 end
 
--- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
--- failed to format: unknown constant 'Lean.Meta._root_.Lean.Parser.Command.registerSimpAttr'
-/-- Simp attribute for lemmas about `is_R_or_C` -/ register_simp_attr is_R_or_C_simps
-
 variable {K E : Type _} [IsROrC K]
 
 namespace IsROrC

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

@@ -50,7 +50,6 @@ open scoped BigOperators
 
 section
 
--- mathport name: expr𝓚
 local notation "𝓚" => algebraMap ℝ _
 
 open scoped ComplexConjugate
@@ -92,19 +91,25 @@ namespace IsROrC
 
 open scoped ComplexConjugate
 
+#print IsROrC.algebraMapCoe /-
 /- The priority must be set at 900 to ensure that coercions are tried in the right order.
 See Note [coercion into rings], or `data/nat/cast.lean` for more details. -/
 noncomputable instance (priority := 900) algebraMapCoe : CoeTC ℝ K :=
   ⟨algebraMap ℝ K⟩
 #align is_R_or_C.algebra_map_coe IsROrC.algebraMapCoe
+-/
 
+#print IsROrC.ofReal_alg /-
 theorem ofReal_alg (x : ℝ) : (x : K) = x • (1 : K) :=
   Algebra.algebraMap_eq_smul_one x
 #align is_R_or_C.of_real_alg IsROrC.ofReal_alg
+-/
 
+#print IsROrC.real_smul_eq_coe_mul /-
 theorem real_smul_eq_coe_mul (r : ℝ) (z : K) : r • z = (r : K) * z :=
   Algebra.smul_def r z
 #align is_R_or_C.real_smul_eq_coe_mul IsROrC.real_smul_eq_coe_mul
+-/
 
 #print IsROrC.real_smul_eq_coe_smul /-
 theorem real_smul_eq_coe_smul [AddCommGroup E] [Module K E] [Module ℝ E] [IsScalarTower ℝ K E]
@@ -112,65 +117,91 @@ theorem real_smul_eq_coe_smul [AddCommGroup E] [Module K E] [Module ℝ E] [IsSc
 #align is_R_or_C.real_smul_eq_coe_smul IsROrC.real_smul_eq_coe_smul
 -/
 
+#print IsROrC.algebraMap_eq_ofReal /-
 theorem algebraMap_eq_ofReal : ⇑(algebraMap ℝ K) = coe :=
   rfl
 #align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_ofReal
+-/
 
+#print IsROrC.re_add_im /-
 @[simp, is_R_or_C_simps]
 theorem re_add_im (z : K) : (re z : K) + im z * i = z :=
   IsROrC.re_add_im_ax z
 #align is_R_or_C.re_add_im IsROrC.re_add_im
+-/
 
+#print IsROrC.ofReal_re /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_re : ∀ r : ℝ, re (r : K) = r :=
   IsROrC.of_real_re_ax
 #align is_R_or_C.of_real_re IsROrC.ofReal_re
+-/
 
+#print IsROrC.ofReal_im /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_im : ∀ r : ℝ, im (r : K) = 0 :=
   IsROrC.of_real_im_ax
 #align is_R_or_C.of_real_im IsROrC.ofReal_im
+-/
 
+#print IsROrC.mul_re /-
 @[simp, is_R_or_C_simps]
 theorem mul_re : ∀ z w : K, re (z * w) = re z * re w - im z * im w :=
   IsROrC.mul_re_ax
 #align is_R_or_C.mul_re IsROrC.mul_re
+-/
 
+#print IsROrC.mul_im /-
 @[simp, is_R_or_C_simps]
 theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
   IsROrC.mul_im_ax
 #align is_R_or_C.mul_im IsROrC.mul_im
+-/
 
+#print IsROrC.ext_iff /-
 theorem ext_iff {z w : K} : z = w ↔ re z = re w ∧ im z = im w :=
   ⟨fun h => h ▸ ⟨rfl, rfl⟩, fun ⟨h₁, h₂⟩ => re_add_im z ▸ re_add_im w ▸ h₁ ▸ h₂ ▸ rfl⟩
 #align is_R_or_C.ext_iff IsROrC.ext_iff
+-/
 
+#print IsROrC.ext /-
 theorem ext {z w : K} (hre : re z = re w) (him : im z = im w) : z = w :=
   ext_iff.2 ⟨hre, him⟩
 #align is_R_or_C.ext IsROrC.ext
+-/
 
+#print IsROrC.ofReal_zero /-
 @[norm_cast]
 theorem ofReal_zero : ((0 : ℝ) : K) = 0 :=
   algebraMap.coe_zero
 #align is_R_or_C.of_real_zero IsROrC.ofReal_zero
+-/
 
+#print IsROrC.zero_re' /-
 @[is_R_or_C_simps]
 theorem zero_re' : re (0 : K) = (0 : ℝ) :=
   map_zero re
 #align is_R_or_C.zero_re' IsROrC.zero_re'
+-/
 
+#print IsROrC.ofReal_one /-
 @[norm_cast]
 theorem ofReal_one : ((1 : ℝ) : K) = 1 :=
   map_one (algebraMap ℝ K)
 #align is_R_or_C.of_real_one IsROrC.ofReal_one
+-/
 
+#print IsROrC.one_re /-
 @[simp, is_R_or_C_simps]
 theorem one_re : re (1 : K) = 1 := by rw [← of_real_one, of_real_re]
 #align is_R_or_C.one_re IsROrC.one_re
+-/
 
+#print IsROrC.one_im /-
 @[simp, is_R_or_C_simps]
 theorem one_im : im (1 : K) = 0 := by rw [← of_real_one, of_real_im]
 #align is_R_or_C.one_im IsROrC.one_im
+-/
 
 #print IsROrC.ofReal_injective /-
 theorem ofReal_injective : Function.Injective (coe : ℝ → K) :=
@@ -185,57 +216,79 @@ theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
 #align is_R_or_C.of_real_inj IsROrC.ofReal_inj
 -/
 
+#print IsROrC.bit0_re /-
 @[simp, is_R_or_C_simps]
 theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_re IsROrC.bit0_re
+-/
 
+#print IsROrC.bit1_re /-
 @[simp, is_R_or_C_simps]
 theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_add, bit0_re, one_re]
 #align is_R_or_C.bit1_re IsROrC.bit1_re
+-/
 
+#print IsROrC.bit0_im /-
 @[simp, is_R_or_C_simps]
 theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_im IsROrC.bit0_im
+-/
 
+#print IsROrC.bit1_im /-
 @[simp, is_R_or_C_simps]
 theorem bit1_im (z : K) : im (bit1 z) = bit0 (im z) := by
   simp only [bit1, map_add, bit0_im, one_im, add_zero]
 #align is_R_or_C.bit1_im IsROrC.bit1_im
+-/
 
+#print IsROrC.ofReal_eq_zero /-
 theorem ofReal_eq_zero {x : ℝ} : (x : K) = 0 ↔ x = 0 :=
   algebraMap.lift_map_eq_zero_iff x
 #align is_R_or_C.of_real_eq_zero IsROrC.ofReal_eq_zero
+-/
 
+#print IsROrC.ofReal_ne_zero /-
 theorem ofReal_ne_zero {x : ℝ} : (x : K) ≠ 0 ↔ x ≠ 0 :=
   ofReal_eq_zero.Not
 #align is_R_or_C.of_real_ne_zero IsROrC.ofReal_ne_zero
+-/
 
+#print IsROrC.ofReal_add /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : K) = r + s :=
   algebraMap.coe_add _ _
 #align is_R_or_C.of_real_add IsROrC.ofReal_add
+-/
 
+#print IsROrC.ofReal_bit0 /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
   ofReal_add _ _
 #align is_R_or_C.of_real_bit0 IsROrC.ofReal_bit0
+-/
 
+#print IsROrC.ofReal_bit1 /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
   map_bit1 (algebraMap ℝ K) r
 #align is_R_or_C.of_real_bit1 IsROrC.ofReal_bit1
+-/
 
+#print IsROrC.ofReal_neg /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : K) = -r :=
   algebraMap.coe_neg r
 #align is_R_or_C.of_real_neg IsROrC.ofReal_neg
+-/
 
+#print IsROrC.ofReal_sub /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
   map_sub (algebraMap ℝ K) r s
 #align is_R_or_C.of_real_sub IsROrC.ofReal_sub
+-/
 
 #print IsROrC.ofReal_sum /-
 @[simp, is_R_or_C_simps, norm_cast]
@@ -245,21 +298,27 @@ theorem ofReal_sum {α : Type _} (s : Finset α) (f : α → ℝ) :
 #align is_R_or_C.of_real_sum IsROrC.ofReal_sum
 -/
 
+#print IsROrC.ofReal_finsupp_sum /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_finsupp_sum {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.Sum fun a b => g a b : ℝ) : K) = f.Sum fun a b => (g a b : K) :=
   map_finsupp_sum (algebraMap ℝ K) f g
 #align is_R_or_C.of_real_finsupp_sum IsROrC.ofReal_finsupp_sum
+-/
 
+#print IsROrC.ofReal_mul /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : K) = r * s :=
   algebraMap.coe_mul _ _
 #align is_R_or_C.of_real_mul IsROrC.ofReal_mul
+-/
 
+#print IsROrC.ofReal_pow /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
   map_pow (algebraMap ℝ K) r n
 #align is_R_or_C.of_real_pow IsROrC.ofReal_pow
+-/
 
 #print IsROrC.ofReal_prod /-
 @[simp, is_R_or_C_simps, norm_cast]
@@ -269,144 +328,197 @@ theorem ofReal_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
 #align is_R_or_C.of_real_prod IsROrC.ofReal_prod
 -/
 
+#print IsROrC.ofReal_finsupp_prod /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.Prod fun a b => g a b : ℝ) : K) = f.Prod fun a b => (g a b : K) :=
   RingHom.map_finsupp_prod _ f g
 #align is_R_or_C.of_real_finsupp_prod IsROrC.ofReal_finsupp_prod
+-/
 
+#print IsROrC.real_smul_ofReal /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem real_smul_ofReal (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
   real_smul_eq_coe_mul _ _
 #align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofReal
+-/
 
+#print IsROrC.ofReal_mul_re /-
 @[is_R_or_C_simps]
 theorem ofReal_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
   simp only [mul_re, of_real_im, MulZeroClass.zero_mul, of_real_re, sub_zero]
 #align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_re
+-/
 
+#print IsROrC.ofReal_mul_im /-
 @[is_R_or_C_simps]
 theorem ofReal_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
   simp only [add_zero, of_real_im, MulZeroClass.zero_mul, of_real_re, mul_im]
 #align is_R_or_C.of_real_mul_im IsROrC.ofReal_mul_im
+-/
 
+#print IsROrC.smul_re /-
 @[is_R_or_C_simps]
 theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
   rw [real_smul_eq_coe_mul, of_real_mul_re]
 #align is_R_or_C.smul_re IsROrC.smul_re
+-/
 
+#print IsROrC.smul_im /-
 @[is_R_or_C_simps]
 theorem smul_im (r : ℝ) (z : K) : im (r • z) = r * im z := by
   rw [real_smul_eq_coe_mul, of_real_mul_im]
 #align is_R_or_C.smul_im IsROrC.smul_im
+-/
 
+#print IsROrC.norm_ofReal /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem norm_ofReal (r : ℝ) : ‖(r : K)‖ = |r| :=
   norm_algebraMap' K r
 #align is_R_or_C.norm_of_real IsROrC.norm_ofReal
+-/
 
 /-! ### Characteristic zero -/
 
 
+#print IsROrC.charZero_isROrC /-
 -- see Note [lower instance priority]
 /-- ℝ and ℂ are both of characteristic zero.  -/
 instance (priority := 100) charZero_isROrC : CharZero K :=
   (RingHom.charZero_iff (algebraMap ℝ K).Injective).1 inferInstance
 #align is_R_or_C.char_zero_R_or_C IsROrC.charZero_isROrC
+-/
 
 /-! ### The imaginary unit, `I` -/
 
 
+#print IsROrC.I_re /-
 /-- The imaginary unit. -/
 @[simp, is_R_or_C_simps]
 theorem I_re : re (i : K) = 0 :=
   i_re_ax
 #align is_R_or_C.I_re IsROrC.I_re
+-/
 
+#print IsROrC.I_im /-
 @[simp, is_R_or_C_simps]
 theorem I_im (z : K) : im z * im (i : K) = im z :=
   mul_im_i_ax z
 #align is_R_or_C.I_im IsROrC.I_im
+-/
 
+#print IsROrC.I_im' /-
 @[simp, is_R_or_C_simps]
 theorem I_im' (z : K) : im (i : K) * im z = im z := by rw [mul_comm, I_im _]
 #align is_R_or_C.I_im' IsROrC.I_im'
+-/
 
+#print IsROrC.I_mul_re /-
 @[simp, is_R_or_C_simps]
 theorem I_mul_re (z : K) : re (i * z) = -im z := by
   simp only [I_re, zero_sub, I_im', MulZeroClass.zero_mul, mul_re]
 #align is_R_or_C.I_mul_re IsROrC.I_mul_re
+-/
 
+#print IsROrC.I_mul_I /-
 theorem I_mul_I : (i : K) = 0 ∨ (i : K) * i = -1 :=
   i_mul_i_ax
 #align is_R_or_C.I_mul_I IsROrC.I_mul_I
+-/
 
+#print IsROrC.conj_re /-
 @[simp, is_R_or_C_simps]
 theorem conj_re (z : K) : re (conj z) = re z :=
   IsROrC.conj_re_ax z
 #align is_R_or_C.conj_re IsROrC.conj_re
+-/
 
+#print IsROrC.conj_im /-
 @[simp, is_R_or_C_simps]
 theorem conj_im (z : K) : im (conj z) = -im z :=
   IsROrC.conj_im_ax z
 #align is_R_or_C.conj_im IsROrC.conj_im
+-/
 
+#print IsROrC.conj_I /-
 @[simp, is_R_or_C_simps]
 theorem conj_I : conj (i : K) = -i :=
   IsROrC.conj_i_ax
 #align is_R_or_C.conj_I IsROrC.conj_I
+-/
 
+#print IsROrC.conj_ofReal /-
 @[simp, is_R_or_C_simps]
 theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) := by rw [ext_iff];
   simp only [of_real_im, conj_im, eq_self_iff_true, conj_re, and_self_iff, neg_zero]
 #align is_R_or_C.conj_of_real IsROrC.conj_ofReal
+-/
 
+#print IsROrC.conj_bit0 /-
 @[simp, is_R_or_C_simps]
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
   map_bit0 _ _
 #align is_R_or_C.conj_bit0 IsROrC.conj_bit0
+-/
 
+#print IsROrC.conj_bit1 /-
 @[simp, is_R_or_C_simps]
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
   map_bit1 _ _
 #align is_R_or_C.conj_bit1 IsROrC.conj_bit1
+-/
 
+#print IsROrC.conj_neg_I /-
 @[simp, is_R_or_C_simps]
 theorem conj_neg_I : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
 #align is_R_or_C.conj_neg_I IsROrC.conj_neg_I
+-/
 
+#print IsROrC.conj_eq_re_sub_im /-
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
   (congr_arg conj (re_add_im z).symm).trans <| by
     rw [map_add, map_mul, conj_I, conj_of_real, conj_of_real, mul_neg, sub_eq_add_neg]
 #align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_im
+-/
 
+#print IsROrC.sub_conj /-
 theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
   by
   nth_rw 1 [← re_add_im z]
   rw [conj_eq_re_sub_im, add_sub_sub_cancel, ← two_mul, mul_assoc]
 #align is_R_or_C.sub_conj IsROrC.sub_conj
+-/
 
+#print IsROrC.conj_smul /-
 @[is_R_or_C_simps]
 theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
   rw [conj_eq_re_sub_im, conj_eq_re_sub_im, smul_re, smul_im, of_real_mul, of_real_mul,
     real_smul_eq_coe_mul, mul_sub, mul_assoc]
 #align is_R_or_C.conj_smul IsROrC.conj_smul
+-/
 
+#print IsROrC.add_conj /-
 theorem add_conj (z : K) : z + conj z = 2 * re z :=
   calc
     z + conj z = re z + im z * i + (re z - im z * i) := by rw [re_add_im, conj_eq_re_sub_im]
     _ = 2 * re z := by rw [add_add_sub_cancel, two_mul]
 #align is_R_or_C.add_conj IsROrC.add_conj
+-/
 
+#print IsROrC.re_eq_add_conj /-
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
   rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
 #align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
+-/
 
+#print IsROrC.im_eq_conj_sub /-
 theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
   rw [← neg_inj, ← of_real_neg, ← I_mul_re, re_eq_add_conj, map_mul, conj_I, ← neg_div, ← mul_neg,
     neg_sub, mul_sub, neg_mul, sub_eq_add_neg]
 #align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_sub
+-/
 
+#print IsROrC.is_real_TFAE /-
 /-- There are several equivalent ways to say that a number `z` is in fact a real number. -/
 theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] :=
   by
@@ -421,31 +533,42 @@ theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(r
   tfae_have 2 → 1; exact fun ⟨r, hr⟩ => hr ▸ conj_of_real _
   tfae_finish
 #align is_R_or_C.is_real_tfae IsROrC.is_real_TFAE
+-/
 
+#print IsROrC.conj_eq_iff_real /-
 theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
   ((is_real_TFAE z).out 0 1).trans <| by simp only [eq_comm]
 #align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_real
+-/
 
+#print IsROrC.conj_eq_iff_re /-
 theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
   (is_real_TFAE z).out 0 2
 #align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
+-/
 
+#print IsROrC.conj_eq_iff_im /-
 theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
   (is_real_TFAE z).out 0 3
 #align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_im
+-/
 
+#print IsROrC.star_def /-
 @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
   rfl
 #align is_R_or_C.star_def IsROrC.star_def
+-/
 
 variable (K)
 
+#print IsROrC.conjToRingEquiv /-
 /-- Conjugation as a ring equivalence. This is used to convert the inner product into a
 sesquilinear product. -/
 abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
   starRingEquiv
 #align is_R_or_C.conj_to_ring_equiv IsROrC.conjToRingEquiv
+-/
 
 variable {K}
 
@@ -459,93 +582,132 @@ def normSq : K →*₀ ℝ where
 #align is_R_or_C.norm_sq IsROrC.normSq
 -/
 
+#print IsROrC.normSq_apply /-
 theorem normSq_apply (z : K) : normSq z = re z * re z + im z * im z :=
   rfl
 #align is_R_or_C.norm_sq_apply IsROrC.normSq_apply
+-/
 
+#print IsROrC.norm_sq_eq_def /-
 theorem norm_sq_eq_def {z : K} : ‖z‖ ^ 2 = re z * re z + im z * im z :=
   norm_sq_eq_def_ax z
 #align is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_def
+-/
 
+#print IsROrC.normSq_eq_def' /-
 theorem normSq_eq_def' (z : K) : normSq z = ‖z‖ ^ 2 :=
   norm_sq_eq_def.symm
 #align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'
+-/
 
+#print IsROrC.normSq_zero /-
 @[is_R_or_C_simps]
 theorem normSq_zero : normSq (0 : K) = 0 :=
   normSq.map_zero
 #align is_R_or_C.norm_sq_zero IsROrC.normSq_zero
+-/
 
+#print IsROrC.normSq_one /-
 @[is_R_or_C_simps]
 theorem normSq_one : normSq (1 : K) = 1 :=
   normSq.map_one
 #align is_R_or_C.norm_sq_one IsROrC.normSq_one
+-/
 
+#print IsROrC.normSq_nonneg /-
 theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
 #align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonneg
+-/
 
+#print IsROrC.normSq_eq_zero /-
 @[simp, is_R_or_C_simps]
 theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 := by rw [norm_sq_eq_def']; simp [sq]
 #align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zero
+-/
 
+#print IsROrC.normSq_pos /-
 @[simp, is_R_or_C_simps]
 theorem normSq_pos {z : K} : 0 < normSq z ↔ z ≠ 0 := by
   rw [lt_iff_le_and_ne, Ne, eq_comm] <;> simp [norm_sq_nonneg]
 #align is_R_or_C.norm_sq_pos IsROrC.normSq_pos
+-/
 
+#print IsROrC.normSq_neg /-
 @[simp, is_R_or_C_simps]
 theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [norm_sq_eq_def', norm_neg]
 #align is_R_or_C.norm_sq_neg IsROrC.normSq_neg
+-/
 
+#print IsROrC.normSq_conj /-
 @[simp, is_R_or_C_simps]
 theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
   simp only [norm_sq_apply, neg_mul, mul_neg, neg_neg, is_R_or_C_simps]
 #align is_R_or_C.norm_sq_conj IsROrC.normSq_conj
+-/
 
+#print IsROrC.normSq_mul /-
 @[simp, is_R_or_C_simps]
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
 #align is_R_or_C.norm_sq_mul IsROrC.normSq_mul
+-/
 
+#print IsROrC.normSq_add /-
 theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) := by
   simp only [norm_sq_apply, map_add, mul_neg, sub_neg_eq_add, is_R_or_C_simps]; ring
 #align is_R_or_C.norm_sq_add IsROrC.normSq_add
+-/
 
+#print IsROrC.re_sq_le_normSq /-
 theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
 #align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSq
+-/
 
+#print IsROrC.im_sq_le_normSq /-
 theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
 #align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
+-/
 
+#print IsROrC.mul_conj /-
 theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
   simp only [map_add, add_zero, ext_iff, add_left_inj, mul_eq_mul_left_iff, MulZeroClass.zero_mul,
     add_comm, true_or_iff, eq_self_iff_true, mul_neg, add_right_neg, zero_add, norm_sq_apply,
     mul_comm, and_self_iff, neg_neg, MulZeroClass.mul_zero, sub_eq_neg_add, neg_zero,
     is_R_or_C_simps]
 #align is_R_or_C.mul_conj IsROrC.mul_conj
+-/
 
+#print IsROrC.conj_mul /-
 theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
 #align is_R_or_C.conj_mul IsROrC.conj_mul
+-/
 
+#print IsROrC.normSq_sub /-
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [norm_sq_add, sub_eq_add_neg, RingEquiv.map_neg, mul_neg, norm_sq_neg, map_neg]
 #align is_R_or_C.norm_sq_sub IsROrC.normSq_sub
+-/
 
+#print IsROrC.sqrt_normSq_eq_norm /-
 theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
   rw [norm_sq_eq_def', Real.sqrt_sq (norm_nonneg _)]
 #align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_norm
+-/
 
 /-! ### Inversion -/
 
 
+#print IsROrC.ofReal_inv /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = r⁻¹ :=
   map_inv₀ (algebraMap ℝ K) r
 #align is_R_or_C.of_real_inv IsROrC.ofReal_inv
+-/
 
+#print IsROrC.inv_def /-
 theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
   by
   rcases eq_or_ne z 0 with (rfl | h₀)
@@ -554,40 +716,55 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
     rw [← mul_assoc, mul_conj, of_real_inv, ← norm_sq_eq_def', mul_inv_cancel]
     rwa [of_real_ne_zero, Ne.def, norm_sq_eq_zero]
 #align is_R_or_C.inv_def IsROrC.inv_def
+-/
 
+#print IsROrC.inv_re /-
 @[simp, is_R_or_C_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
   rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_re, conj_re, div_eq_inv_mul]
 #align is_R_or_C.inv_re IsROrC.inv_re
+-/
 
+#print IsROrC.inv_im /-
 @[simp, is_R_or_C_simps]
 theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
   rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_im, conj_im, div_eq_inv_mul]
 #align is_R_or_C.inv_im IsROrC.inv_im
+-/
 
+#print IsROrC.div_re /-
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, neg_mul, mul_neg, neg_neg, map_neg,
     is_R_or_C_simps]
 #align is_R_or_C.div_re IsROrC.div_re
+-/
 
+#print IsROrC.div_im /-
 theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm, neg_mul, mul_neg, map_neg,
     is_R_or_C_simps]
 #align is_R_or_C.div_im IsROrC.div_im
+-/
 
+#print IsROrC.conj_inv /-
 @[simp, is_R_or_C_simps]
 theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align is_R_or_C.conj_inv IsROrC.conj_inv
+-/
 
+#print IsROrC.ofReal_div /-
 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
   map_div₀ (algebraMap ℝ K) r s
 #align is_R_or_C.of_real_div IsROrC.ofReal_div
+-/
 
+#print IsROrC.div_re_ofReal /-
 theorem div_re_ofReal {z : K} {r : ℝ} : re (z / r) = re z / r := by
   rw [div_eq_inv_mul, div_eq_inv_mul, ← of_real_inv, of_real_mul_re]
 #align is_R_or_C.div_re_of_real IsROrC.div_re_ofReal
+-/
 
 #print IsROrC.ofReal_zpow /-
 @[simp, norm_cast, is_R_or_C_simps]
@@ -596,34 +773,46 @@ theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : K) = r ^ n :=
 #align is_R_or_C.of_real_zpow IsROrC.ofReal_zpow
 -/
 
+#print IsROrC.I_mul_I_of_nonzero /-
 theorem I_mul_I_of_nonzero : (i : K) ≠ 0 → (i : K) * i = -1 :=
   i_mul_i_ax.resolve_left
 #align is_R_or_C.I_mul_I_of_nonzero IsROrC.I_mul_I_of_nonzero
+-/
 
+#print IsROrC.inv_I /-
 @[simp, is_R_or_C_simps]
 theorem inv_I : (i : K)⁻¹ = -i := by
   by_cases h : (I : K) = 0
   · simp [h]
   · field_simp [I_mul_I_of_nonzero h]
 #align is_R_or_C.inv_I IsROrC.inv_I
+-/
 
+#print IsROrC.div_I /-
 @[simp, is_R_or_C_simps]
 theorem div_I (z : K) : z / i = -(z * i) := by rw [div_eq_mul_inv, inv_I, mul_neg]
 #align is_R_or_C.div_I IsROrC.div_I
+-/
 
+#print IsROrC.normSq_inv /-
 @[simp, is_R_or_C_simps]
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ (@normSq K _) z
 #align is_R_or_C.norm_sq_inv IsROrC.normSq_inv
+-/
 
+#print IsROrC.normSq_div /-
 @[simp, is_R_or_C_simps]
 theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ (@normSq K _) z w
 #align is_R_or_C.norm_sq_div IsROrC.normSq_div
+-/
 
+#print IsROrC.norm_conj /-
 @[simp, is_R_or_C_simps]
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_norm_sq_eq_norm, norm_sq_conj]
 #align is_R_or_C.norm_conj IsROrC.norm_conj
+-/
 
 instance (priority := 100) : CstarRing K
     where norm_star_mul_self x := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) norm_conj
@@ -631,157 +820,219 @@ instance (priority := 100) : CstarRing K
 /-! ### Cast lemmas -/
 
 
+#print IsROrC.ofReal_natCast /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_natCast (n : ℕ) : ((n : ℝ) : K) = n :=
   map_natCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_nat_cast IsROrC.ofReal_natCast
+-/
 
+#print IsROrC.natCast_re /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem natCast_re (n : ℕ) : re (n : K) = n := by rw [← of_real_nat_cast, of_real_re]
 #align is_R_or_C.nat_cast_re IsROrC.natCast_re
+-/
 
+#print IsROrC.natCast_im /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem natCast_im (n : ℕ) : im (n : K) = 0 := by rw [← of_real_nat_cast, of_real_im]
 #align is_R_or_C.nat_cast_im IsROrC.natCast_im
+-/
 
+#print IsROrC.ofReal_intCast /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : K) = n :=
   map_intCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_int_cast IsROrC.ofReal_intCast
+-/
 
+#print IsROrC.intCast_re /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem intCast_re (n : ℤ) : re (n : K) = n := by rw [← of_real_int_cast, of_real_re]
 #align is_R_or_C.int_cast_re IsROrC.intCast_re
+-/
 
+#print IsROrC.intCast_im /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem intCast_im (n : ℤ) : im (n : K) = 0 := by rw [← of_real_int_cast, of_real_im]
 #align is_R_or_C.int_cast_im IsROrC.intCast_im
+-/
 
+#print IsROrC.ofReal_ratCast /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_ratCast (n : ℚ) : ((n : ℝ) : K) = n :=
   map_ratCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_rat_cast IsROrC.ofReal_ratCast
+-/
 
+#print IsROrC.ratCast_re /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ratCast_re (q : ℚ) : re (q : K) = q := by rw [← of_real_rat_cast, of_real_re]
 #align is_R_or_C.rat_cast_re IsROrC.ratCast_re
+-/
 
+#print IsROrC.ratCast_im /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ratCast_im (q : ℚ) : im (q : K) = 0 := by rw [← of_real_rat_cast, of_real_im]
 #align is_R_or_C.rat_cast_im IsROrC.ratCast_im
+-/
 
 /-! ### Norm -/
 
 
+#print IsROrC.norm_of_nonneg /-
 theorem norm_of_nonneg {r : ℝ} (h : 0 ≤ r) : ‖(r : K)‖ = r :=
   (norm_ofReal _).trans (abs_of_nonneg h)
 #align is_R_or_C.norm_of_nonneg IsROrC.norm_of_nonneg
+-/
 
+#print IsROrC.norm_natCast /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n := by rw [← of_real_nat_cast];
   exact norm_of_nonneg (Nat.cast_nonneg n)
 #align is_R_or_C.norm_nat_cast IsROrC.norm_natCast
+-/
 
+#print IsROrC.mul_self_norm /-
 theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [norm_sq_eq_def', sq]
 #align is_R_or_C.mul_self_norm IsROrC.mul_self_norm
+-/
 
 attribute [is_R_or_C_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
 
+#print IsROrC.norm_two /-
 @[simp, is_R_or_C_simps]
 theorem norm_two : ‖(2 : K)‖ = 2 := by rw [← Nat.cast_two, norm_nat_cast, Nat.cast_two]
 #align is_R_or_C.norm_two IsROrC.norm_two
+-/
 
+#print IsROrC.abs_re_le_norm /-
 theorem abs_re_le_norm (z : K) : |re z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (re z)) (norm_nonneg _), abs_mul_abs_self,
       mul_self_norm] <;>
     apply re_sq_le_norm_sq
 #align is_R_or_C.abs_re_le_norm IsROrC.abs_re_le_norm
+-/
 
+#print IsROrC.abs_im_le_norm /-
 theorem abs_im_le_norm (z : K) : |im z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (im z)) (norm_nonneg _), abs_mul_abs_self,
       mul_self_norm] <;>
     apply im_sq_le_norm_sq
 #align is_R_or_C.abs_im_le_norm IsROrC.abs_im_le_norm
+-/
 
+#print IsROrC.norm_re_le_norm /-
 theorem norm_re_le_norm (z : K) : ‖re z‖ ≤ ‖z‖ :=
   abs_re_le_norm z
 #align is_R_or_C.norm_re_le_norm IsROrC.norm_re_le_norm
+-/
 
+#print IsROrC.norm_im_le_norm /-
 theorem norm_im_le_norm (z : K) : ‖im z‖ ≤ ‖z‖ :=
   abs_im_le_norm z
 #align is_R_or_C.norm_im_le_norm IsROrC.norm_im_le_norm
+-/
 
+#print IsROrC.re_le_norm /-
 theorem re_le_norm (z : K) : re z ≤ ‖z‖ :=
   (abs_le.1 (abs_re_le_norm z)).2
 #align is_R_or_C.re_le_norm IsROrC.re_le_norm
+-/
 
+#print IsROrC.im_le_norm /-
 theorem im_le_norm (z : K) : im z ≤ ‖z‖ :=
   (abs_le.1 (abs_im_le_norm _)).2
 #align is_R_or_C.im_le_norm IsROrC.im_le_norm
+-/
 
+#print IsROrC.im_eq_zero_of_le /-
 theorem im_eq_zero_of_le {a : K} (h : ‖a‖ ≤ re a) : im a = 0 := by
   simpa only [mul_self_norm a, norm_sq_apply, self_eq_add_right, mul_self_eq_zero] using
     congr_arg (fun z => z * z) ((re_le_norm a).antisymm h)
 #align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_le
+-/
 
+#print IsROrC.re_eq_self_of_le /-
 theorem re_eq_self_of_le {a : K} (h : ‖a‖ ≤ re a) : (re a : K) = a := by
   rw [(is_real_tfae a).out 2 3, im_eq_zero_of_le h]
 #align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_le
+-/
 
 open IsAbsoluteValue
 
+#print IsROrC.abs_re_div_norm_le_one /-
 theorem abs_re_div_norm_le_one (z : K) : |re z / ‖z‖| ≤ 1 :=
   by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_re_le_norm _) (norm_nonneg _)
 #align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_one
+-/
 
+#print IsROrC.abs_im_div_norm_le_one /-
 theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
   by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_im_le_norm _) (norm_nonneg _)
 #align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
+-/
 
+#print IsROrC.re_eq_norm_of_mul_conj /-
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, of_real_re, norm_of_real, abs_of_nonneg (norm_sq_nonneg _)]
 #align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj
+-/
 
+#print IsROrC.norm_sq_re_add_conj /-
 theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
   rw [add_conj, norm_mul, norm_two, norm_of_real, two_mul (re x : K), map_add, of_real_re, ←
     two_mul, mul_pow, mul_pow, sq_abs]
 #align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conj
+-/
 
+#print IsROrC.norm_sq_re_conj_add /-
 theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2 := by
   rw [add_comm, norm_sq_re_add_conj]
 #align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_add
+-/
 
 /-! ### Cauchy sequences -/
 
 
+#print IsROrC.isCauSeq_re /-
 theorem isCauSeq_re (f : CauSeq K norm) : IsCauSeq abs fun n => re (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_re_le_norm (f j - f i)) (H _ ij)
 #align is_R_or_C.is_cau_seq_re IsROrC.isCauSeq_re
+-/
 
+#print IsROrC.isCauSeq_im /-
 theorem isCauSeq_im (f : CauSeq K norm) : IsCauSeq abs fun n => im (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_im_le_norm (f j - f i)) (H _ ij)
 #align is_R_or_C.is_cau_seq_im IsROrC.isCauSeq_im
+-/
 
+#print IsROrC.cauSeqRe /-
 /-- The real part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_re f⟩
 #align is_R_or_C.cau_seq_re IsROrC.cauSeqRe
+-/
 
+#print IsROrC.cauSeqIm /-
 /-- The imaginary part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_im f⟩
 #align is_R_or_C.cau_seq_im IsROrC.cauSeqIm
+-/
 
+#print IsROrC.isCauSeq_norm /-
 theorem isCauSeq_norm {f : ℕ → K} (hf : IsCauSeq norm f) : IsCauSeq abs (norm ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
   ⟨i, fun j hj => lt_of_le_of_lt (abs_norm_sub_norm_le _ _) (hi j hj)⟩
 #align is_R_or_C.is_cau_seq_norm IsROrC.isCauSeq_norm
+-/
 
 end IsROrC
 
@@ -823,41 +1074,47 @@ open scoped ComplexConjugate
 
 section CleanupLemmas
 
--- mathport name: exprreR
 local notation "reR" => @IsROrC.re ℝ _
 
--- mathport name: exprimR
 local notation "imR" => @IsROrC.im ℝ _
 
--- mathport name: exprIR
 local notation "IR" => @IsROrC.i ℝ _
 
--- mathport name: exprnorm_sqR
 local notation "norm_sqR" => @IsROrC.normSq ℝ _
 
+#print IsROrC.re_to_real /-
 @[simp, is_R_or_C_simps]
 theorem re_to_real {x : ℝ} : reR x = x :=
   rfl
 #align is_R_or_C.re_to_real IsROrC.re_to_real
+-/
 
+#print IsROrC.im_to_real /-
 @[simp, is_R_or_C_simps]
 theorem im_to_real {x : ℝ} : imR x = 0 :=
   rfl
 #align is_R_or_C.im_to_real IsROrC.im_to_real
+-/
 
+#print IsROrC.conj_to_real /-
 @[simp, is_R_or_C_simps]
 theorem conj_to_real {x : ℝ} : conj x = x :=
   rfl
 #align is_R_or_C.conj_to_real IsROrC.conj_to_real
+-/
 
+#print IsROrC.I_to_real /-
 @[simp, is_R_or_C_simps]
 theorem I_to_real : IR = 0 :=
   rfl
 #align is_R_or_C.I_to_real IsROrC.I_to_real
+-/
 
+#print IsROrC.normSq_to_real /-
 @[simp, is_R_or_C_simps]
 theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [IsROrC.normSq]
 #align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_real
+-/
 
 #print IsROrC.ofReal_real_eq_id /-
 @[simp]
@@ -877,10 +1134,12 @@ def reLm : K →ₗ[ℝ] ℝ :=
 #align is_R_or_C.re_lm IsROrC.reLm
 -/
 
+#print IsROrC.reLm_coe /-
 @[simp, is_R_or_C_simps]
 theorem reLm_coe : (reLm : K → ℝ) = re :=
   rfl
 #align is_R_or_C.re_lm_coe IsROrC.reLm_coe
+-/
 
 #print IsROrC.reClm /-
 /-- The real part in a `is_R_or_C` field, as a continuous linear map. -/
@@ -896,15 +1155,19 @@ theorem reClm_coe : ((reClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
 #align is_R_or_C.re_clm_coe IsROrC.reClm_coe
 -/
 
+#print IsROrC.reClm_apply /-
 @[simp, is_R_or_C_simps]
 theorem reClm_apply : ((reClm : K →L[ℝ] ℝ) : K → ℝ) = re :=
   rfl
 #align is_R_or_C.re_clm_apply IsROrC.reClm_apply
+-/
 
+#print IsROrC.continuous_re /-
 @[continuity]
 theorem continuous_re : Continuous (re : K → ℝ) :=
   reClm.Continuous
 #align is_R_or_C.continuous_re IsROrC.continuous_re
+-/
 
 #print IsROrC.imLm /-
 /-- The imaginary part in a `is_R_or_C` field, as a linear map. -/
@@ -913,10 +1176,12 @@ def imLm : K →ₗ[ℝ] ℝ :=
 #align is_R_or_C.im_lm IsROrC.imLm
 -/
 
+#print IsROrC.imLm_coe /-
 @[simp, is_R_or_C_simps]
 theorem imLm_coe : (imLm : K → ℝ) = im :=
   rfl
 #align is_R_or_C.im_lm_coe IsROrC.imLm_coe
+-/
 
 #print IsROrC.imClm /-
 /-- The imaginary part in a `is_R_or_C` field, as a continuous linear map. -/
@@ -932,15 +1197,19 @@ theorem imClm_coe : ((imClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
 #align is_R_or_C.im_clm_coe IsROrC.imClm_coe
 -/
 
+#print IsROrC.imClm_apply /-
 @[simp, is_R_or_C_simps]
 theorem imClm_apply : ((imClm : K →L[ℝ] ℝ) : K → ℝ) = im :=
   rfl
 #align is_R_or_C.im_clm_apply IsROrC.imClm_apply
+-/
 
+#print IsROrC.continuous_im /-
 @[continuity]
 theorem continuous_im : Continuous (im : K → ℝ) :=
   imClm.Continuous
 #align is_R_or_C.continuous_im IsROrC.continuous_im
+-/
 
 #print IsROrC.conjAe /-
 /-- Conjugate as an `ℝ`-algebra equivalence -/
@@ -953,10 +1222,12 @@ def conjAe : K ≃ₐ[ℝ] K :=
 #align is_R_or_C.conj_ae IsROrC.conjAe
 -/
 
+#print IsROrC.conjAe_coe /-
 @[simp, is_R_or_C_simps]
 theorem conjAe_coe : (conjAe : K → K) = conj :=
   rfl
 #align is_R_or_C.conj_ae_coe IsROrC.conjAe_coe
+-/
 
 #print IsROrC.conjLie /-
 /-- Conjugate as a linear isometry -/
@@ -965,10 +1236,12 @@ noncomputable def conjLie : K ≃ₗᵢ[ℝ] K :=
 #align is_R_or_C.conj_lie IsROrC.conjLie
 -/
 
+#print IsROrC.conjLie_apply /-
 @[simp, is_R_or_C_simps]
 theorem conjLie_apply : (conjLie : K → K) = conj :=
   rfl
 #align is_R_or_C.conj_lie_apply IsROrC.conjLie_apply
+-/
 
 #print IsROrC.conjCle /-
 /-- Conjugate as a continuous linear equivalence -/
@@ -984,18 +1257,22 @@ theorem conjCle_coe : (@conjCle K _).toLinearEquiv = conjAe.toLinearEquiv :=
 #align is_R_or_C.conj_cle_coe IsROrC.conjCle_coe
 -/
 
+#print IsROrC.conjCle_apply /-
 @[simp, is_R_or_C_simps]
 theorem conjCle_apply : (conjCle : K → K) = conj :=
   rfl
 #align is_R_or_C.conj_cle_apply IsROrC.conjCle_apply
+-/
 
 instance (priority := 100) : ContinuousStar K :=
   ⟨conjLie.Continuous⟩
 
+#print IsROrC.continuous_conj /-
 @[continuity]
 theorem continuous_conj : Continuous (conj : K → K) :=
   continuous_star
 #align is_R_or_C.continuous_conj IsROrC.continuous_conj
+-/
 
 #print IsROrC.ofRealAm /-
 /-- The `ℝ → K` coercion, as a linear map -/
@@ -1004,10 +1281,12 @@ noncomputable def ofRealAm : ℝ →ₐ[ℝ] K :=
 #align is_R_or_C.of_real_am IsROrC.ofRealAm
 -/
 
+#print IsROrC.ofRealAm_coe /-
 @[simp, is_R_or_C_simps]
 theorem ofRealAm_coe : (ofRealAm : ℝ → K) = coe :=
   rfl
 #align is_R_or_C.of_real_am_coe IsROrC.ofRealAm_coe
+-/
 
 #print IsROrC.ofRealLi /-
 /-- The ℝ → K coercion, as a linear isometry -/
@@ -1018,10 +1297,12 @@ noncomputable def ofRealLi : ℝ →ₗᵢ[ℝ] K
 #align is_R_or_C.of_real_li IsROrC.ofRealLi
 -/
 
+#print IsROrC.ofRealLi_apply /-
 @[simp, is_R_or_C_simps]
 theorem ofRealLi_apply : (ofRealLi : ℝ → K) = coe :=
   rfl
 #align is_R_or_C.of_real_li_apply IsROrC.ofRealLi_apply
+-/
 
 #print IsROrC.ofRealClm /-
 /-- The `ℝ → K` coercion, as a continuous linear map -/
@@ -1037,10 +1318,12 @@ theorem ofRealClm_coe : (@ofRealClm K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinear
 #align is_R_or_C.of_real_clm_coe IsROrC.ofRealClm_coe
 -/
 
+#print IsROrC.ofRealClm_apply /-
 @[simp, is_R_or_C_simps]
 theorem ofRealClm_apply : (ofRealClm : ℝ → K) = coe :=
   rfl
 #align is_R_or_C.of_real_clm_apply IsROrC.ofRealClm_apply
+-/
 
 #print IsROrC.continuous_ofReal /-
 @[continuity]
@@ -1049,10 +1332,12 @@ theorem continuous_ofReal : Continuous (coe : ℝ → K) :=
 #align is_R_or_C.continuous_of_real IsROrC.continuous_ofReal
 -/
 
+#print IsROrC.continuous_normSq /-
 @[continuity]
 theorem continuous_normSq : Continuous (normSq : K → ℝ) :=
   (continuous_re.mul continuous_re).add (continuous_im.mul continuous_im)
 #align is_R_or_C.continuous_norm_sq IsROrC.continuous_normSq
+-/
 
 end LinearMaps
 

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

@@ -396,7 +396,6 @@ theorem add_conj (z : K) : z + conj z = 2 * re z :=
   calc
     z + conj z = re z + im z * i + (re z - im z * i) := by rw [re_add_im, conj_eq_re_sub_im]
     _ = 2 * re z := by rw [add_add_sub_cancel, two_mul]
-    
 #align is_R_or_C.add_conj IsROrC.add_conj
 
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by

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

@@ -82,11 +82,8 @@ class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebr
 
 end
 
-/- failed to parenthesize: unknown constant 'Lean.Meta._root_.Lean.Parser.Command.registerSimpAttr'
-[PrettyPrinter.parenthesize.input] (Lean.Meta._root_.Lean.Parser.Command.registerSimpAttr
-     [(Command.docComment "/--" "Simp attribute for lemmas about `is_R_or_C` -/")]
-     "register_simp_attr"
-     `is_R_or_C_simps)-/-- failed to format: unknown constant 'Lean.Meta._root_.Lean.Parser.Command.registerSimpAttr'
+-- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
+-- failed to format: unknown constant 'Lean.Meta._root_.Lean.Parser.Command.registerSimpAttr'
 /-- Simp attribute for lemmas about `is_R_or_C` -/ register_simp_attr is_R_or_C_simps
 
 variable {K E : Type _} [IsROrC K]

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

@@ -60,7 +60,7 @@ open scoped ComplexConjugate
 This typeclass captures properties shared by ℝ and ℂ, with an API that closely matches that of ℂ.
 -/
 class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebra ℝ K,
-  CompleteSpace K where
+    CompleteSpace K where
   re : K →+ ℝ
   im : K →+ ℝ
   i : K

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

@@ -1008,12 +1008,10 @@ noncomputable def ofRealAm : ℝ →ₐ[ℝ] K :=
 #align is_R_or_C.of_real_am IsROrC.ofRealAm
 -/
 
-#print IsROrC.ofRealAm_coe /-
 @[simp, is_R_or_C_simps]
 theorem ofRealAm_coe : (ofRealAm : ℝ → K) = coe :=
   rfl
 #align is_R_or_C.of_real_am_coe IsROrC.ofRealAm_coe
--/
 
 #print IsROrC.ofRealLi /-
 /-- The ℝ → K coercion, as a linear isometry -/

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

@@ -46,14 +46,14 @@ A few lemmas requiring heavier imports are in `data.is_R_or_C.lemmas`.
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 section
 
 -- mathport name: expr𝓚
 local notation "𝓚" => algebraMap ℝ _
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 #print IsROrC /-
 /--
@@ -93,7 +93,7 @@ variable {K E : Type _} [IsROrC K]
 
 namespace IsROrC
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 /- The priority must be set at 900 to ensure that coercions are tried in the right order.
 See Note [coercion into rings], or `data/nat/cast.lean` for more details. -/
@@ -823,7 +823,7 @@ end Instances
 
 namespace IsROrC
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 section CleanupLemmas
 

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

@@ -95,34 +95,16 @@ namespace IsROrC
 
 open ComplexConjugate
 
-/- warning: is_R_or_C.algebra_map_coe -> IsROrC.algebraMapCoe is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], CoeTCₓ.{1, succ u1} Real K
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], CoeTC.{1, succ u1} Real K
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.algebra_map_coe IsROrC.algebraMapCoeₓ'. -/
 /- The priority must be set at 900 to ensure that coercions are tried in the right order.
 See Note [coercion into rings], or `data/nat/cast.lean` for more details. -/
 noncomputable instance (priority := 900) algebraMapCoe : CoeTC ℝ K :=
   ⟨algebraMap ℝ K⟩
 #align is_R_or_C.algebra_map_coe IsROrC.algebraMapCoe
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_alg IsROrC.ofReal_algₓ'. -/
 theorem ofReal_alg (x : ℝ) : (x : K) = x • (1 : K) :=
   Algebra.algebraMap_eq_smul_one x
 #align is_R_or_C.of_real_alg IsROrC.ofReal_alg
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.real_smul_eq_coe_mul IsROrC.real_smul_eq_coe_mulₓ'. -/
 theorem real_smul_eq_coe_mul (r : ℝ) (z : K) : r • z = (r : K) * z :=
   Algebra.smul_def r z
 #align is_R_or_C.real_smul_eq_coe_mul IsROrC.real_smul_eq_coe_mul
@@ -133,125 +115,62 @@ theorem real_smul_eq_coe_smul [AddCommGroup E] [Module K E] [Module ℝ E] [IsSc
 #align is_R_or_C.real_smul_eq_coe_smul IsROrC.real_smul_eq_coe_smul
 -/
 
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 theorem algebraMap_eq_ofReal : ⇑(algebraMap ℝ K) = coe :=
   rfl
 #align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_ofReal
 
-/- warning: is_R_or_C.re_add_im -> IsROrC.re_add_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_add_im IsROrC.re_add_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem re_add_im (z : K) : (re z : K) + im z * i = z :=
   IsROrC.re_add_im_ax z
 #align is_R_or_C.re_add_im IsROrC.re_add_im
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_re : ∀ r : ℝ, re (r : K) = r :=
   IsROrC.of_real_re_ax
 #align is_R_or_C.of_real_re IsROrC.ofReal_re
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_im : ∀ r : ℝ, im (r : K) = 0 :=
   IsROrC.of_real_im_ax
 #align is_R_or_C.of_real_im IsROrC.ofReal_im
 
-/- warning: is_R_or_C.mul_re -> IsROrC.mul_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_re IsROrC.mul_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem mul_re : ∀ z w : K, re (z * w) = re z * re w - im z * im w :=
   IsROrC.mul_re_ax
 #align is_R_or_C.mul_re IsROrC.mul_re
 
-/- warning: is_R_or_C.mul_im -> IsROrC.mul_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_im IsROrC.mul_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
   IsROrC.mul_im_ax
 #align is_R_or_C.mul_im IsROrC.mul_im
 
-/- warning: is_R_or_C.ext_iff -> IsROrC.ext_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.ext_iff IsROrC.ext_iffₓ'. -/
 theorem ext_iff {z w : K} : z = w ↔ re z = re w ∧ im z = im w :=
   ⟨fun h => h ▸ ⟨rfl, rfl⟩, fun ⟨h₁, h₂⟩ => re_add_im z ▸ re_add_im w ▸ h₁ ▸ h₂ ▸ rfl⟩
 #align is_R_or_C.ext_iff IsROrC.ext_iff
 
-/- warning: is_R_or_C.ext -> IsROrC.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.ext IsROrC.extₓ'. -/
 theorem ext {z w : K} (hre : re z = re w) (him : im z = im w) : z = w :=
   ext_iff.2 ⟨hre, him⟩
 #align is_R_or_C.ext IsROrC.ext
 
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 @[norm_cast]
 theorem ofReal_zero : ((0 : ℝ) : K) = 0 :=
   algebraMap.coe_zero
 #align is_R_or_C.of_real_zero IsROrC.ofReal_zero
 
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 @[is_R_or_C_simps]
 theorem zero_re' : re (0 : K) = (0 : ℝ) :=
   map_zero re
 #align is_R_or_C.zero_re' IsROrC.zero_re'
 
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 @[norm_cast]
 theorem ofReal_one : ((1 : ℝ) : K) = 1 :=
   map_one (algebraMap ℝ K)
 #align is_R_or_C.of_real_one IsROrC.ofReal_one
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.one_re IsROrC.one_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem one_re : re (1 : K) = 1 := by rw [← of_real_one, of_real_re]
 #align is_R_or_C.one_re IsROrC.one_re
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.one_im IsROrC.one_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem one_im : im (1 : K) = 0 := by rw [← of_real_one, of_real_im]
 #align is_R_or_C.one_im IsROrC.one_im
@@ -269,107 +188,53 @@ theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
 #align is_R_or_C.of_real_inj IsROrC.ofReal_inj
 -/
 
-/- warning: is_R_or_C.bit0_re -> IsROrC.bit0_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit0_re IsROrC.bit0_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_re IsROrC.bit0_re
 
-/- warning: is_R_or_C.bit1_re -> IsROrC.bit1_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit1_re IsROrC.bit1_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_add, bit0_re, one_re]
 #align is_R_or_C.bit1_re IsROrC.bit1_re
 
-/- warning: is_R_or_C.bit0_im -> IsROrC.bit0_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit0_im IsROrC.bit0_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_im IsROrC.bit0_im
 
-/- warning: is_R_or_C.bit1_im -> IsROrC.bit1_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit1_im IsROrC.bit1_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit1_im (z : K) : im (bit1 z) = bit0 (im z) := by
   simp only [bit1, map_add, bit0_im, one_im, add_zero]
 #align is_R_or_C.bit1_im IsROrC.bit1_im
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_eq_zero IsROrC.ofReal_eq_zeroₓ'. -/
 theorem ofReal_eq_zero {x : ℝ} : (x : K) = 0 ↔ x = 0 :=
   algebraMap.lift_map_eq_zero_iff x
 #align is_R_or_C.of_real_eq_zero IsROrC.ofReal_eq_zero
 
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 theorem ofReal_ne_zero {x : ℝ} : (x : K) ≠ 0 ↔ x ≠ 0 :=
   ofReal_eq_zero.Not
 #align is_R_or_C.of_real_ne_zero IsROrC.ofReal_ne_zero
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : K) = r + s :=
   algebraMap.coe_add _ _
 #align is_R_or_C.of_real_add IsROrC.ofReal_add
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
   ofReal_add _ _
 #align is_R_or_C.of_real_bit0 IsROrC.ofReal_bit0
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
   map_bit1 (algebraMap ℝ K) r
 #align is_R_or_C.of_real_bit1 IsROrC.ofReal_bit1
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : K) = -r :=
   algebraMap.coe_neg r
 #align is_R_or_C.of_real_neg IsROrC.ofReal_neg
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
   map_sub (algebraMap ℝ K) r s
@@ -383,35 +248,17 @@ theorem ofReal_sum {α : Type _} (s : Finset α) (f : α → ℝ) :
 #align is_R_or_C.of_real_sum IsROrC.ofReal_sum
 -/
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_finsupp_sum {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.Sum fun a b => g a b : ℝ) : K) = f.Sum fun a b => (g a b : K) :=
   map_finsupp_sum (algebraMap ℝ K) f g
 #align is_R_or_C.of_real_finsupp_sum IsROrC.ofReal_finsupp_sum
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : K) = r * s :=
   algebraMap.coe_mul _ _
 #align is_R_or_C.of_real_mul IsROrC.ofReal_mul
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
   map_pow (algebraMap ℝ K) r n
@@ -425,67 +272,37 @@ theorem ofReal_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
 #align is_R_or_C.of_real_prod IsROrC.ofReal_prod
 -/
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.Prod fun a b => g a b : ℝ) : K) = f.Prod fun a b => (g a b : K) :=
   RingHom.map_finsupp_prod _ f g
 #align is_R_or_C.of_real_finsupp_prod IsROrC.ofReal_finsupp_prod
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem real_smul_ofReal (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
   real_smul_eq_coe_mul _ _
 #align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofReal
 
-/- warning: is_R_or_C.of_real_mul_re -> IsROrC.ofReal_mul_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_reₓ'. -/
 @[is_R_or_C_simps]
 theorem ofReal_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
   simp only [mul_re, of_real_im, MulZeroClass.zero_mul, of_real_re, sub_zero]
 #align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_re
 
-/- warning: is_R_or_C.of_real_mul_im -> IsROrC.ofReal_mul_im is a dubious translation:
-<too large>
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 @[is_R_or_C_simps]
 theorem ofReal_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
   simp only [add_zero, of_real_im, MulZeroClass.zero_mul, of_real_re, mul_im]
 #align is_R_or_C.of_real_mul_im IsROrC.ofReal_mul_im
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.smul_re IsROrC.smul_reₓ'. -/
 @[is_R_or_C_simps]
 theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
   rw [real_smul_eq_coe_mul, of_real_mul_re]
 #align is_R_or_C.smul_re IsROrC.smul_re
 
-/- warning: is_R_or_C.smul_im -> IsROrC.smul_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.smul_im IsROrC.smul_imₓ'. -/
 @[is_R_or_C_simps]
 theorem smul_im (r : ℝ) (z : K) : im (r • z) = r * im z := by
   rw [real_smul_eq_coe_mul, of_real_mul_im]
 #align is_R_or_C.smul_im IsROrC.smul_im
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem norm_ofReal (r : ℝ) : ‖(r : K)‖ = |r| :=
   norm_algebraMap' K r
@@ -494,12 +311,6 @@ theorem norm_ofReal (r : ℝ) : ‖(r : K)‖ = |r| :=
 /-! ### Characteristic zero -/
 
 
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 -- see Note [lower instance priority]
 /-- ℝ and ℂ are both of characteristic zero.  -/
 instance (priority := 100) charZero_isROrC : CharZero K :=
@@ -509,144 +320,81 @@ instance (priority := 100) charZero_isROrC : CharZero K :=
 /-! ### The imaginary unit, `I` -/
 
 
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 /-- The imaginary unit. -/
 @[simp, is_R_or_C_simps]
 theorem I_re : re (i : K) = 0 :=
   i_re_ax
 #align is_R_or_C.I_re IsROrC.I_re
 
-/- warning: is_R_or_C.I_im -> IsROrC.I_im is a dubious translation:
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 @[simp, is_R_or_C_simps]
 theorem I_im (z : K) : im z * im (i : K) = im z :=
   mul_im_i_ax z
 #align is_R_or_C.I_im IsROrC.I_im
 
-/- warning: is_R_or_C.I_im' -> IsROrC.I_im' is a dubious translation:
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 @[simp, is_R_or_C_simps]
 theorem I_im' (z : K) : im (i : K) * im z = im z := by rw [mul_comm, I_im _]
 #align is_R_or_C.I_im' IsROrC.I_im'
 
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 @[simp, is_R_or_C_simps]
 theorem I_mul_re (z : K) : re (i * z) = -im z := by
   simp only [I_re, zero_sub, I_im', MulZeroClass.zero_mul, mul_re]
 #align is_R_or_C.I_mul_re IsROrC.I_mul_re
 
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 theorem I_mul_I : (i : K) = 0 ∨ (i : K) * i = -1 :=
   i_mul_i_ax
 #align is_R_or_C.I_mul_I IsROrC.I_mul_I
 
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 @[simp, is_R_or_C_simps]
 theorem conj_re (z : K) : re (conj z) = re z :=
   IsROrC.conj_re_ax z
 #align is_R_or_C.conj_re IsROrC.conj_re
 
-/- warning: is_R_or_C.conj_im -> IsROrC.conj_im is a dubious translation:
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 @[simp, is_R_or_C_simps]
 theorem conj_im (z : K) : im (conj z) = -im z :=
   IsROrC.conj_im_ax z
 #align is_R_or_C.conj_im IsROrC.conj_im
 
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.I.{u1} K _inst_1)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) _inst_1)))))) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) _inst_1))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_I IsROrC.conj_Iₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_I : conj (i : K) = -i :=
   IsROrC.conj_i_ax
 #align is_R_or_C.conj_I IsROrC.conj_I
 
-/- warning: is_R_or_C.conj_of_real -> IsROrC.conj_ofReal is a dubious translation:
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-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.ofReal.{u1} K _inst_1 r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1 r)) (IsROrC.ofReal.{u1} K _inst_1 r)
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_of_real IsROrC.conj_ofRealₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) := by rw [ext_iff];
   simp only [of_real_im, conj_im, eq_self_iff_true, conj_re, and_self_iff, neg_zero]
 #align is_R_or_C.conj_of_real IsROrC.conj_ofReal
 
-/- warning: is_R_or_C.conj_bit0 -> IsROrC.conj_bit0 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_bit0 IsROrC.conj_bit0ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
   map_bit0 _ _
 #align is_R_or_C.conj_bit0 IsROrC.conj_bit0
 
-/- warning: is_R_or_C.conj_bit1 -> IsROrC.conj_bit1 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_bit1 IsROrC.conj_bit1ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
   map_bit1 _ _
 #align is_R_or_C.conj_bit1 IsROrC.conj_bit1
 
-/- warning: is_R_or_C.conj_neg_I -> IsROrC.conj_neg_I is a dubious translation:
-lean 3 declaration is
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.I.{u1} K _inst_1))) (IsROrC.I.{u1} K _inst_1)
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_neg_I IsROrC.conj_neg_Iₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_neg_I : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
 #align is_R_or_C.conj_neg_I IsROrC.conj_neg_I
 
-/- warning: is_R_or_C.conj_eq_re_sub_im -> IsROrC.conj_eq_re_sub_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_imₓ'. -/
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
   (congr_arg conj (re_add_im z).symm).trans <| by
     rw [map_add, map_mul, conj_I, conj_of_real, conj_of_real, mul_neg, sub_eq_add_neg]
 #align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_im
 
-/- warning: is_R_or_C.sub_conj -> IsROrC.sub_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.sub_conj IsROrC.sub_conjₓ'. -/
 theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
   by
   nth_rw 1 [← re_add_im z]
   rw [conj_eq_re_sub_im, add_sub_sub_cancel, ← two_mul, mul_assoc]
 #align is_R_or_C.sub_conj IsROrC.sub_conj
 
-/- warning: is_R_or_C.conj_smul -> IsROrC.conj_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_smul IsROrC.conj_smulₓ'. -/
 @[is_R_or_C_simps]
 theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
   rw [conj_eq_re_sub_im, conj_eq_re_sub_im, smul_re, smul_im, of_real_mul, of_real_mul,
     real_smul_eq_coe_mul, mul_sub, mul_assoc]
 #align is_R_or_C.conj_smul IsROrC.conj_smul
 
-/- warning: is_R_or_C.add_conj -> IsROrC.add_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.add_conj IsROrC.add_conjₓ'. -/
 theorem add_conj (z : K) : z + conj z = 2 * re z :=
   calc
     z + conj z = re z + im z * i + (re z - im z * i) := by rw [re_add_im, conj_eq_re_sub_im]
@@ -654,24 +402,15 @@ theorem add_conj (z : K) : z + conj z = 2 * re z :=
     
 #align is_R_or_C.add_conj IsROrC.add_conj
 
-/- warning: is_R_or_C.re_eq_add_conj -> IsROrC.re_eq_add_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conjₓ'. -/
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
   rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
 #align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
 
-/- warning: is_R_or_C.im_eq_conj_sub -> IsROrC.im_eq_conj_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_subₓ'. -/
 theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
   rw [← neg_inj, ← of_real_neg, ← I_mul_re, re_eq_add_conj, map_mul, conj_I, ← neg_div, ← mul_neg,
     neg_sub, mul_sub, neg_mul, sub_eq_add_neg]
 #align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_sub
 
-/- warning: is_R_or_C.is_real_tfae -> IsROrC.is_real_TFAE is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_real_tfae IsROrC.is_real_TFAEₓ'. -/
 /-- There are several equivalent ways to say that a number `z` is in fact a real number. -/
 theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] :=
   by
@@ -687,36 +426,18 @@ theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(r
   tfae_finish
 #align is_R_or_C.is_real_tfae IsROrC.is_real_TFAE
 
-/- warning: is_R_or_C.conj_eq_iff_real -> IsROrC.conj_eq_iff_real is a dubious translation:
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{succ u1} K z (IsROrC.ofReal.{u1} K _inst_1 r)))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_realₓ'. -/
 theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
   ((is_real_TFAE z).out 0 1).trans <| by simp only [eq_comm]
 #align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_real
 
-/- warning: is_R_or_C.conj_eq_iff_re -> IsROrC.conj_eq_iff_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_reₓ'. -/
 theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
   (is_real_TFAE z).out 0 2
 #align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
 
-/- warning: is_R_or_C.conj_eq_iff_im -> IsROrC.conj_eq_iff_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_imₓ'. -/
 theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
   (is_real_TFAE z).out 0 3
 #align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_im
 
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 @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
   rfl
@@ -724,12 +445,6 @@ theorem star_def : (Star.star : K → K) = conj :=
 
 variable (K)
 
-/- warning: is_R_or_C.conj_to_ring_equiv -> IsROrC.conjToRingEquiv is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_to_ring_equiv IsROrC.conjToRingEquivₓ'. -/
 /-- Conjugation as a ring equivalence. This is used to convert the inner product into a
 sesquilinear product. -/
 abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
@@ -748,130 +463,67 @@ def normSq : K →*₀ ℝ where
 #align is_R_or_C.norm_sq IsROrC.normSq
 -/
 
-/- warning: is_R_or_C.norm_sq_apply -> IsROrC.normSq_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_apply IsROrC.normSq_applyₓ'. -/
 theorem normSq_apply (z : K) : normSq z = re z * re z + im z * im z :=
   rfl
 #align is_R_or_C.norm_sq_apply IsROrC.normSq_apply
 
-/- warning: is_R_or_C.norm_sq_eq_def -> IsROrC.norm_sq_eq_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_defₓ'. -/
 theorem norm_sq_eq_def {z : K} : ‖z‖ ^ 2 = re z * re z + im z * im z :=
   norm_sq_eq_def_ax z
 #align is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_def
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'ₓ'. -/
 theorem normSq_eq_def' (z : K) : normSq z = ‖z‖ ^ 2 :=
   norm_sq_eq_def.symm
 #align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_zero IsROrC.normSq_zeroₓ'. -/
 @[is_R_or_C_simps]
 theorem normSq_zero : normSq (0 : K) = 0 :=
   normSq.map_zero
 #align is_R_or_C.norm_sq_zero IsROrC.normSq_zero
 
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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instOneReal))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_one IsROrC.normSq_oneₓ'. -/
 @[is_R_or_C_simps]
 theorem normSq_one : normSq (1 : K) = 1 :=
   normSq.map_one
 #align is_R_or_C.norm_sq_one IsROrC.normSq_one
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonnegₓ'. -/
 theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
 #align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonneg
 
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 @[simp, is_R_or_C_simps]
 theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 := by rw [norm_sq_eq_def']; simp [sq]
 #align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zero
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_pos IsROrC.normSq_posₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_pos {z : K} : 0 < normSq z ↔ z ≠ 0 := by
   rw [lt_iff_le_and_ne, Ne, eq_comm] <;> simp [norm_sq_nonneg]
 #align is_R_or_C.norm_sq_pos IsROrC.normSq_pos
 
-/- warning: is_R_or_C.norm_sq_neg -> IsROrC.normSq_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_neg IsROrC.normSq_negₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [norm_sq_eq_def', norm_neg]
 #align is_R_or_C.norm_sq_neg IsROrC.normSq_neg
 
-/- warning: is_R_or_C.norm_sq_conj -> IsROrC.normSq_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_conj IsROrC.normSq_conjₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
   simp only [norm_sq_apply, neg_mul, mul_neg, neg_neg, is_R_or_C_simps]
 #align is_R_or_C.norm_sq_conj IsROrC.normSq_conj
 
-/- warning: is_R_or_C.norm_sq_mul -> IsROrC.normSq_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_mul IsROrC.normSq_mulₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
 #align is_R_or_C.norm_sq_mul IsROrC.normSq_mul
 
-/- warning: is_R_or_C.norm_sq_add -> IsROrC.normSq_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_add IsROrC.normSq_addₓ'. -/
 theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) := by
   simp only [norm_sq_apply, map_add, mul_neg, sub_neg_eq_add, is_R_or_C_simps]; ring
 #align is_R_or_C.norm_sq_add IsROrC.normSq_add
 
-/- warning: is_R_or_C.re_sq_le_norm_sq -> IsROrC.re_sq_le_normSq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
 #align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSq
 
-/- warning: is_R_or_C.im_sq_le_norm_sq -> IsROrC.im_sq_le_normSq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
 #align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
 
-/- warning: is_R_or_C.mul_conj -> IsROrC.mul_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_conj IsROrC.mul_conjₓ'. -/
 theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
   simp only [map_add, add_zero, ext_iff, add_left_inj, mul_eq_mul_left_iff, MulZeroClass.zero_mul,
     add_comm, true_or_iff, eq_self_iff_true, mul_neg, add_right_neg, zero_add, norm_sq_apply,
@@ -879,25 +531,13 @@ theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
     is_R_or_C_simps]
 #align is_R_or_C.mul_conj IsROrC.mul_conj
 
-/- warning: is_R_or_C.conj_mul -> IsROrC.conj_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_mul IsROrC.conj_mulₓ'. -/
 theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
 #align is_R_or_C.conj_mul IsROrC.conj_mul
 
-/- warning: is_R_or_C.norm_sq_sub -> IsROrC.normSq_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_sub IsROrC.normSq_subₓ'. -/
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [norm_sq_add, sub_eq_add_neg, RingEquiv.map_neg, mul_neg, norm_sq_neg, map_neg]
 #align is_R_or_C.norm_sq_sub IsROrC.normSq_sub
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_normₓ'. -/
 theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
   rw [norm_sq_eq_def', Real.sqrt_sq (norm_nonneg _)]
 #align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_norm
@@ -905,23 +545,11 @@ theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
 /-! ### Inversion -/
 
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = r⁻¹ :=
   map_inv₀ (algebraMap ℝ K) r
 #align is_R_or_C.of_real_inv IsROrC.ofReal_inv
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_def IsROrC.inv_defₓ'. -/
 theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
   by
   rcases eq_or_ne z 0 with (rfl | h₀)
@@ -931,60 +559,36 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
     rwa [of_real_ne_zero, Ne.def, norm_sq_eq_zero]
 #align is_R_or_C.inv_def IsROrC.inv_def
 
-/- warning: is_R_or_C.inv_re -> IsROrC.inv_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_re IsROrC.inv_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
   rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_re, conj_re, div_eq_inv_mul]
 #align is_R_or_C.inv_re IsROrC.inv_re
 
-/- warning: is_R_or_C.inv_im -> IsROrC.inv_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_im IsROrC.inv_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
   rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_im, conj_im, div_eq_inv_mul]
 #align is_R_or_C.inv_im IsROrC.inv_im
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_re IsROrC.div_reₓ'. -/
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, neg_mul, mul_neg, neg_neg, map_neg,
     is_R_or_C_simps]
 #align is_R_or_C.div_re IsROrC.div_re
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_im IsROrC.div_imₓ'. -/
 theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm, neg_mul, mul_neg, map_neg,
     is_R_or_C_simps]
 #align is_R_or_C.div_im IsROrC.div_im
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_inv IsROrC.conj_invₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align is_R_or_C.conj_inv IsROrC.conj_inv
 
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 @[simp, norm_cast, is_R_or_C_simps]
 theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
   map_div₀ (algebraMap ℝ K) r s
 #align is_R_or_C.of_real_div IsROrC.ofReal_div
 
-/- warning: is_R_or_C.div_re_of_real -> IsROrC.div_re_ofReal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_re_of_real IsROrC.div_re_ofRealₓ'. -/
 theorem div_re_ofReal {z : K} {r : ℝ} : re (z / r) = re z / r := by
   rw [div_eq_inv_mul, div_eq_inv_mul, ← of_real_inv, of_real_mul_re]
 #align is_R_or_C.div_re_of_real IsROrC.div_re_ofReal
@@ -996,22 +600,10 @@ theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : K) = r ^ n :=
 #align is_R_or_C.of_real_zpow IsROrC.ofReal_zpow
 -/
 
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 theorem I_mul_I_of_nonzero : (i : K) ≠ 0 → (i : K) * i = -1 :=
   i_mul_i_ax.resolve_left
 #align is_R_or_C.I_mul_I_of_nonzero IsROrC.I_mul_I_of_nonzero
 
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 @[simp, is_R_or_C_simps]
 theorem inv_I : (i : K)⁻¹ = -i := by
   by_cases h : (I : K) = 0
@@ -1019,38 +611,20 @@ theorem inv_I : (i : K)⁻¹ = -i := by
   · field_simp [I_mul_I_of_nonzero h]
 #align is_R_or_C.inv_I IsROrC.inv_I
 
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 @[simp, is_R_or_C_simps]
 theorem div_I (z : K) : z / i = -(z * i) := by rw [div_eq_mul_inv, inv_I, mul_neg]
 #align is_R_or_C.div_I IsROrC.div_I
 
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-<too large>
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 @[simp, is_R_or_C_simps]
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ (@normSq K _) z
 #align is_R_or_C.norm_sq_inv IsROrC.normSq_inv
 
-/- warning: is_R_or_C.norm_sq_div -> IsROrC.normSq_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_div IsROrC.normSq_divₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ (@normSq K _) z w
 #align is_R_or_C.norm_sq_div IsROrC.normSq_div
 
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
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 @[simp, is_R_or_C_simps]
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_norm_sq_eq_norm, norm_sq_conj]
 #align is_R_or_C.norm_conj IsROrC.norm_conj
@@ -1061,95 +635,41 @@ instance (priority := 100) : CstarRing K
 /-! ### Cast lemmas -/
 
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_natCast (n : ℕ) : ((n : ℝ) : K) = n :=
   map_natCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_nat_cast IsROrC.ofReal_natCast
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem natCast_re (n : ℕ) : re (n : K) = n := by rw [← of_real_nat_cast, of_real_re]
 #align is_R_or_C.nat_cast_re IsROrC.natCast_re
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem natCast_im (n : ℕ) : im (n : K) = 0 := by rw [← of_real_nat_cast, of_real_im]
 #align is_R_or_C.nat_cast_im IsROrC.natCast_im
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : K) = n :=
   map_intCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_int_cast IsROrC.ofReal_intCast
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem intCast_re (n : ℤ) : re (n : K) = n := by rw [← of_real_int_cast, of_real_re]
 #align is_R_or_C.int_cast_re IsROrC.intCast_re
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem intCast_im (n : ℤ) : im (n : K) = 0 := by rw [← of_real_int_cast, of_real_im]
 #align is_R_or_C.int_cast_im IsROrC.intCast_im
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ofReal_ratCast (n : ℚ) : ((n : ℝ) : K) = n :=
   map_ratCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_rat_cast IsROrC.ofReal_ratCast
 
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 @[simp, is_R_or_C_simps, norm_cast]
 theorem ratCast_re (q : ℚ) : re (q : K) = q := by rw [← of_real_rat_cast, of_real_re]
 #align is_R_or_C.rat_cast_re IsROrC.ratCast_re
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.rat_cast_im IsROrC.ratCast_imₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
 theorem ratCast_im (q : ℚ) : im (q : K) = 0 := by rw [← of_real_rat_cast, of_real_im]
 #align is_R_or_C.rat_cast_im IsROrC.ratCast_im
@@ -1157,165 +677,84 @@ theorem ratCast_im (q : ℚ) : im (q : K) = 0 := by rw [← of_real_rat_cast, of
 /-! ### Norm -/
 
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_of_nonneg IsROrC.norm_of_nonnegₓ'. -/
 theorem norm_of_nonneg {r : ℝ} (h : 0 ≤ r) : ‖(r : K)‖ = r :=
   (norm_ofReal _).trans (abs_of_nonneg h)
 #align is_R_or_C.norm_of_nonneg IsROrC.norm_of_nonneg
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_nat_cast IsROrC.norm_natCastₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
 theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n := by rw [← of_real_nat_cast];
   exact norm_of_nonneg (Nat.cast_nonneg n)
 #align is_R_or_C.norm_nat_cast IsROrC.norm_natCast
 
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 theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [norm_sq_eq_def', sq]
 #align is_R_or_C.mul_self_norm IsROrC.mul_self_norm
 
 attribute [is_R_or_C_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
 
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 @[simp, is_R_or_C_simps]
 theorem norm_two : ‖(2 : K)‖ = 2 := by rw [← Nat.cast_two, norm_nat_cast, Nat.cast_two]
 #align is_R_or_C.norm_two IsROrC.norm_two
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_re_le_norm IsROrC.abs_re_le_normₓ'. -/
 theorem abs_re_le_norm (z : K) : |re z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (re z)) (norm_nonneg _), abs_mul_abs_self,
       mul_self_norm] <;>
     apply re_sq_le_norm_sq
 #align is_R_or_C.abs_re_le_norm IsROrC.abs_re_le_norm
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_im_le_norm IsROrC.abs_im_le_normₓ'. -/
 theorem abs_im_le_norm (z : K) : |im z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (im z)) (norm_nonneg _), abs_mul_abs_self,
       mul_self_norm] <;>
     apply im_sq_le_norm_sq
 #align is_R_or_C.abs_im_le_norm IsROrC.abs_im_le_norm
 
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 theorem norm_re_le_norm (z : K) : ‖re z‖ ≤ ‖z‖ :=
   abs_re_le_norm z
 #align is_R_or_C.norm_re_le_norm IsROrC.norm_re_le_norm
 
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 theorem norm_im_le_norm (z : K) : ‖im z‖ ≤ ‖z‖ :=
   abs_im_le_norm z
 #align is_R_or_C.norm_im_le_norm IsROrC.norm_im_le_norm
 
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 theorem re_le_norm (z : K) : re z ≤ ‖z‖ :=
   (abs_le.1 (abs_re_le_norm z)).2
 #align is_R_or_C.re_le_norm IsROrC.re_le_norm
 
-/- warning: is_R_or_C.im_le_norm -> IsROrC.im_le_norm is a dubious translation:
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-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_le_norm IsROrC.im_le_normₓ'. -/
 theorem im_le_norm (z : K) : im z ≤ ‖z‖ :=
   (abs_le.1 (abs_im_le_norm _)).2
 #align is_R_or_C.im_le_norm IsROrC.im_le_norm
 
-/- warning: is_R_or_C.im_eq_zero_of_le -> IsROrC.im_eq_zero_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_leₓ'. -/
 theorem im_eq_zero_of_le {a : K} (h : ‖a‖ ≤ re a) : im a = 0 := by
   simpa only [mul_self_norm a, norm_sq_apply, self_eq_add_right, mul_self_eq_zero] using
     congr_arg (fun z => z * z) ((re_le_norm a).antisymm h)
 #align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_le
 
-/- warning: is_R_or_C.re_eq_self_of_le -> IsROrC.re_eq_self_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_leₓ'. -/
 theorem re_eq_self_of_le {a : K} (h : ‖a‖ ≤ re a) : (re a : K) = a := by
   rw [(is_real_tfae a).out 2 3, im_eq_zero_of_le h]
 #align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_le
 
 open IsAbsoluteValue
 
-/- warning: is_R_or_C.abs_re_div_norm_le_one -> IsROrC.abs_re_div_norm_le_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_oneₓ'. -/
 theorem abs_re_div_norm_le_one (z : K) : |re z / ‖z‖| ≤ 1 :=
   by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_re_le_norm _) (norm_nonneg _)
 #align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_one
 
-/- warning: is_R_or_C.abs_im_div_norm_le_one -> IsROrC.abs_im_div_norm_le_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_oneₓ'. -/
 theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
   by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_im_le_norm _) (norm_nonneg _)
 #align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
 
-/- warning: is_R_or_C.re_eq_norm_of_mul_conj -> IsROrC.re_eq_norm_of_mul_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conjₓ'. -/
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, of_real_re, norm_of_real, abs_of_nonneg (norm_sq_nonneg _)]
 #align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj
 
-/- warning: is_R_or_C.norm_sq_re_add_conj -> IsROrC.norm_sq_re_add_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conjₓ'. -/
 theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
   rw [add_conj, norm_mul, norm_two, norm_of_real, two_mul (re x : K), map_add, of_real_re, ←
     two_mul, mul_pow, mul_pow, sq_abs]
 #align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conj
 
-/- warning: is_R_or_C.norm_sq_re_conj_add -> IsROrC.norm_sq_re_conj_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_addₓ'. -/
 theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2 := by
   rw [add_comm, norm_sq_re_add_conj]
 #align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_add
@@ -1323,56 +762,26 @@ theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2
 /-! ### Cauchy sequences -/
 
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_cau_seq_re IsROrC.isCauSeq_reₓ'. -/
 theorem isCauSeq_re (f : CauSeq K norm) : IsCauSeq abs fun n => re (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_re_le_norm (f j - f i)) (H _ ij)
 #align is_R_or_C.is_cau_seq_re IsROrC.isCauSeq_re
 
-/- warning: is_R_or_C.is_cau_seq_im -> IsROrC.isCauSeq_im is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_cau_seq_im IsROrC.isCauSeq_imₓ'. -/
 theorem isCauSeq_im (f : CauSeq K norm) : IsCauSeq abs fun n => im (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_im_le_norm (f j - f i)) (H _ ij)
 #align is_R_or_C.is_cau_seq_im IsROrC.isCauSeq_im
 
-/- warning: is_R_or_C.cau_seq_re -> IsROrC.cauSeqRe is a dubious translation:
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-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], (CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.cau_seq_re IsROrC.cauSeqReₓ'. -/
 /-- The real part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_re f⟩
 #align is_R_or_C.cau_seq_re IsROrC.cauSeqRe
 
-/- warning: is_R_or_C.cau_seq_im -> IsROrC.cauSeqIm is a dubious translation:
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-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], (CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.cau_seq_im IsROrC.cauSeqImₓ'. -/
 /-- The imaginary part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_im f⟩
 #align is_R_or_C.cau_seq_im IsROrC.cauSeqIm
 
-/- warning: is_R_or_C.is_cau_seq_norm -> IsROrC.isCauSeq_norm is a dubious translation:
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-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {f : Nat -> K}, (IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, succ u1, 1} Nat K Real (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) f))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_cau_seq_norm IsROrC.isCauSeq_normₓ'. -/
 theorem isCauSeq_norm {f : ℕ → K} (hf : IsCauSeq norm f) : IsCauSeq abs (norm ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
   ⟨i, fun j hj => lt_of_le_of_lt (abs_norm_sub_norm_le _ _) (hi j hj)⟩
@@ -1430,56 +839,26 @@ local notation "IR" => @IsROrC.i ℝ _
 -- mathport name: exprnorm_sqR
 local notation "norm_sqR" => @IsROrC.normSq ℝ _
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_to_real IsROrC.re_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem re_to_real {x : ℝ} : reR x = x :=
   rfl
 #align is_R_or_C.re_to_real IsROrC.re_to_real
 
-/- warning: is_R_or_C.im_to_real -> IsROrC.im_to_real is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Eq.{1} Real (coeFn.{1, 1} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Real -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{0} Real Real.isROrC) x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
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-  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real Real (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{0} Real Real.isROrC) x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) x) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) x) Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_to_real IsROrC.im_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem im_to_real {x : ℝ} : imR x = 0 :=
   rfl
 #align is_R_or_C.im_to_real IsROrC.im_to_real
 
-/- warning: is_R_or_C.conj_to_real -> IsROrC.conj_to_real is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Eq.{1} Real (coeFn.{1, 1} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (fun (_x : RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) => Real -> Real) (RingHom.hasCoeToFun.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (starRingEnd.{0} Real Real.commSemiring Real.starRing) x) x
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_to_real IsROrC.conj_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_to_real {x : ℝ} : conj x = x :=
   rfl
 #align is_R_or_C.conj_to_real IsROrC.conj_to_real
 
-/- warning: is_R_or_C.I_to_real -> IsROrC.I_to_real is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (IsROrC.i.{0} Real Real.isROrC) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
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-  Eq.{1} Real (IsROrC.I.{0} Real Real.isROrC) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_to_real IsROrC.I_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem I_to_real : IR = 0 :=
   rfl
 #align is_R_or_C.I_to_real IsROrC.I_to_real
 
-/- warning: is_R_or_C.norm_sq_to_real -> IsROrC.normSq_to_real is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [IsROrC.normSq]
 #align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_real
@@ -1502,9 +881,6 @@ def reLm : K →ₗ[ℝ] ℝ :=
 #align is_R_or_C.re_lm IsROrC.reLm
 -/
 
-/- warning: is_R_or_C.re_lm_coe -> IsROrC.reLm_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_lm_coe IsROrC.reLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem reLm_coe : (reLm : K → ℝ) = re :=
   rfl
@@ -1524,20 +900,11 @@ theorem reClm_coe : ((reClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
 #align is_R_or_C.re_clm_coe IsROrC.reClm_coe
 -/
 
-/- warning: is_R_or_C.re_clm_apply -> IsROrC.reClm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_clm_apply IsROrC.reClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem reClm_apply : ((reClm : K →L[ℝ] ℝ) : K → ℝ) = re :=
   rfl
 #align is_R_or_C.re_clm_apply IsROrC.reClm_apply
 
-/- warning: is_R_or_C.continuous_re -> IsROrC.continuous_re is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_re IsROrC.continuous_reₓ'. -/
 @[continuity]
 theorem continuous_re : Continuous (re : K → ℝ) :=
   reClm.Continuous
@@ -1550,9 +917,6 @@ def imLm : K →ₗ[ℝ] ℝ :=
 #align is_R_or_C.im_lm IsROrC.imLm
 -/
 
-/- warning: is_R_or_C.im_lm_coe -> IsROrC.imLm_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_lm_coe IsROrC.imLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem imLm_coe : (imLm : K → ℝ) = im :=
   rfl
@@ -1572,20 +936,11 @@ theorem imClm_coe : ((imClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
 #align is_R_or_C.im_clm_coe IsROrC.imClm_coe
 -/
 
-/- warning: is_R_or_C.im_clm_apply -> IsROrC.imClm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_clm_apply IsROrC.imClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem imClm_apply : ((imClm : K →L[ℝ] ℝ) : K → ℝ) = im :=
   rfl
 #align is_R_or_C.im_clm_apply IsROrC.imClm_apply
 
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-Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_im IsROrC.continuous_imₓ'. -/
 @[continuity]
 theorem continuous_im : Continuous (im : K → ℝ) :=
   imClm.Continuous
@@ -1602,9 +957,6 @@ def conjAe : K ≃ₐ[ℝ] K :=
 #align is_R_or_C.conj_ae IsROrC.conjAe
 -/
 
-/- warning: is_R_or_C.conj_ae_coe -> IsROrC.conjAe_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_ae_coe IsROrC.conjAe_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjAe_coe : (conjAe : K → K) = conj :=
   rfl
@@ -1617,9 +969,6 @@ noncomputable def conjLie : K ≃ₗᵢ[ℝ] K :=
 #align is_R_or_C.conj_lie IsROrC.conjLie
 -/
 
-/- warning: is_R_or_C.conj_lie_apply -> IsROrC.conjLie_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_lie_apply IsROrC.conjLie_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjLie_apply : (conjLie : K → K) = conj :=
   rfl
@@ -1639,9 +988,6 @@ theorem conjCle_coe : (@conjCle K _).toLinearEquiv = conjAe.toLinearEquiv :=
 #align is_R_or_C.conj_cle_coe IsROrC.conjCle_coe
 -/
 
-/- warning: is_R_or_C.conj_cle_apply -> IsROrC.conjCle_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_cle_apply IsROrC.conjCle_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjCle_apply : (conjCle : K → K) = conj :=
   rfl
@@ -1650,12 +996,6 @@ theorem conjCle_apply : (conjCle : K → K) = conj :=
 instance (priority := 100) : ContinuousStar K :=
   ⟨conjLie.Continuous⟩
 
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_conj IsROrC.continuous_conjₓ'. -/
 @[continuity]
 theorem continuous_conj : Continuous (conj : K → K) :=
   continuous_star
@@ -1684,9 +1024,6 @@ noncomputable def ofRealLi : ℝ →ₗᵢ[ℝ] K
 #align is_R_or_C.of_real_li IsROrC.ofRealLi
 -/
 
-/- warning: is_R_or_C.of_real_li_apply -> IsROrC.ofRealLi_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_li_apply IsROrC.ofRealLi_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem ofRealLi_apply : (ofRealLi : ℝ → K) = coe :=
   rfl
@@ -1706,9 +1043,6 @@ theorem ofRealClm_coe : (@ofRealClm K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinear
 #align is_R_or_C.of_real_clm_coe IsROrC.ofRealClm_coe
 -/
 
-/- warning: is_R_or_C.of_real_clm_apply -> IsROrC.ofRealClm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_clm_apply IsROrC.ofRealClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem ofRealClm_apply : (ofRealClm : ℝ → K) = coe :=
   rfl
@@ -1721,12 +1055,6 @@ theorem continuous_ofReal : Continuous (coe : ℝ → K) :=
 #align is_R_or_C.continuous_of_real IsROrC.continuous_ofReal
 -/
 
-/- warning: is_R_or_C.continuous_norm_sq -> IsROrC.continuous_normSq is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1))
-Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_norm_sq IsROrC.continuous_normSqₓ'. -/
 @[continuity]
 theorem continuous_normSq : Continuous (normSq : K → ℝ) :=
   (continuous_re.mul continuous_re).add (continuous_im.mul continuous_im)

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

@@ -588,9 +588,7 @@ but is expected to have type
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.ofReal.{u1} K _inst_1 r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1 r)) (IsROrC.ofReal.{u1} K _inst_1 r)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_of_real IsROrC.conj_ofRealₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) :=
-  by
-  rw [ext_iff]
+theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) := by rw [ext_iff];
   simp only [of_real_im, conj_im, eq_self_iff_true, conj_re, and_self_iff, neg_zero]
 #align is_R_or_C.conj_of_real IsROrC.conj_ofReal
 
@@ -746,9 +744,7 @@ def normSq : K →*₀ ℝ where
   toFun z := re z * re z + im z * im z
   map_zero' := by simp only [add_zero, MulZeroClass.mul_zero, map_zero]
   map_one' := by simp only [one_im, add_zero, mul_one, one_re, MulZeroClass.mul_zero]
-  map_mul' z w := by
-    simp only [mul_im, mul_re]
-    ring
+  map_mul' z w := by simp only [mul_im, mul_re]; ring
 #align is_R_or_C.norm_sq IsROrC.normSq
 -/
 
@@ -815,10 +811,7 @@ but is expected to have type
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instZeroReal))) (Eq.{succ u1} K z (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zeroₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 :=
-  by
-  rw [norm_sq_eq_def']
-  simp [sq]
+theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 := by rw [norm_sq_eq_def']; simp [sq]
 #align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zero
 
 /- warning: is_R_or_C.norm_sq_pos -> IsROrC.normSq_pos is a dubious translation:
@@ -858,10 +851,8 @@ theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
 /- warning: is_R_or_C.norm_sq_add -> IsROrC.normSq_add is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_add IsROrC.normSq_addₓ'. -/
-theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) :=
-  by
-  simp only [norm_sq_apply, map_add, mul_neg, sub_neg_eq_add, is_R_or_C_simps]
-  ring
+theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) := by
+  simp only [norm_sq_apply, map_add, mul_neg, sub_neg_eq_add, is_R_or_C_simps]; ring
 #align is_R_or_C.norm_sq_add IsROrC.normSq_add
 
 /- warning: is_R_or_C.re_sq_le_norm_sq -> IsROrC.re_sq_le_normSq is a dubious translation:
@@ -1183,9 +1174,7 @@ but is expected to have type
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{1} Real (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) (Nat.cast.{0} Real Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_nat_cast IsROrC.norm_natCastₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n :=
-  by
-  rw [← of_real_nat_cast]
+theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n := by rw [← of_real_nat_cast];
   exact norm_of_nonneg (Nat.cast_nonneg n)
 #align is_R_or_C.norm_nat_cast IsROrC.norm_natCast
 
@@ -1524,9 +1513,7 @@ theorem reLm_coe : (reLm : K → ℝ) = re :=
 #print IsROrC.reClm /-
 /-- The real part in a `is_R_or_C` field, as a continuous linear map. -/
 noncomputable def reClm : K →L[ℝ] ℝ :=
-  LinearMap.mkContinuous reLm 1 fun x => by
-    rw [one_mul]
-    exact abs_re_le_norm x
+  LinearMap.mkContinuous reLm 1 fun x => by rw [one_mul]; exact abs_re_le_norm x
 #align is_R_or_C.re_clm IsROrC.reClm
 -/
 
@@ -1574,9 +1561,7 @@ theorem imLm_coe : (imLm : K → ℝ) = im :=
 #print IsROrC.imClm /-
 /-- The imaginary part in a `is_R_or_C` field, as a continuous linear map. -/
 noncomputable def imClm : K →L[ℝ] ℝ :=
-  LinearMap.mkContinuous imLm 1 fun x => by
-    rw [one_mul]
-    exact abs_im_le_norm x
+  LinearMap.mkContinuous imLm 1 fun x => by rw [one_mul]; exact abs_im_le_norm x
 #align is_R_or_C.im_clm IsROrC.imClm
 -/
 

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

@@ -144,10 +144,7 @@ theorem algebraMap_eq_ofReal : ⇑(algebraMap ℝ K) = coe :=
 #align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_ofReal
 
 /- warning: is_R_or_C.re_add_im -> IsROrC.re_add_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_add_im IsROrC.re_add_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem re_add_im (z : K) : (re z : K) + im z * i = z :=
@@ -177,10 +174,7 @@ theorem ofReal_im : ∀ r : ℝ, im (r : K) = 0 :=
 #align is_R_or_C.of_real_im IsROrC.ofReal_im
 
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instSubReal) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K 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(AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) w)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_re IsROrC.mul_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem mul_re : ∀ z w : K, re (z * w) = re z * re w - im z * im w :=
@@ -188,10 +182,7 @@ theorem mul_re : ∀ z w : K, re (z * w) = re z * re w - im z * im w :=
 #align is_R_or_C.mul_re IsROrC.mul_re
 
 /- warning: is_R_or_C.mul_im -> IsROrC.mul_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_im IsROrC.mul_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
@@ -199,20 +190,14 @@ theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
 #align is_R_or_C.mul_im IsROrC.mul_im
 
 /- warning: is_R_or_C.ext_iff -> IsROrC.ext_iff is a dubious translation:
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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) w)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.ext_iff IsROrC.ext_iffₓ'. -/
 theorem ext_iff {z w : K} : z = w ↔ re z = re w ∧ im z = im w :=
   ⟨fun h => h ▸ ⟨rfl, rfl⟩, fun ⟨h₁, h₂⟩ => re_add_im z ▸ re_add_im w ▸ h₁ ▸ h₂ ▸ rfl⟩
 #align is_R_or_C.ext_iff IsROrC.ext_iff
 
 /- warning: is_R_or_C.ext -> IsROrC.ext is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.ext IsROrC.extₓ'. -/
 theorem ext {z w : K} (hre : re z = re w) (him : im z = im w) : z = w :=
   ext_iff.2 ⟨hre, him⟩
@@ -285,10 +270,7 @@ theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
 -/
 
 /- warning: is_R_or_C.bit0_re -> IsROrC.bit0_re is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit0_re IsROrC.bit0_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
@@ -296,20 +278,14 @@ theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
 #align is_R_or_C.bit0_re IsROrC.bit0_re
 
 /- warning: is_R_or_C.bit1_re -> IsROrC.bit1_re is a dubious translation:
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(AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instOneReal Real.instAddReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K 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(IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit1_re IsROrC.bit1_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_add, bit0_re, one_re]
 #align is_R_or_C.bit1_re IsROrC.bit1_re
 
 /- warning: is_R_or_C.bit0_im -> IsROrC.bit0_im 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 is_R_or_C.bit0_im IsROrC.bit0_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
@@ -317,10 +293,7 @@ theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
 #align is_R_or_C.bit0_im IsROrC.bit0_im
 
 /- warning: is_R_or_C.bit1_im -> IsROrC.bit1_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit1_im IsROrC.bit1_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit1_im (z : K) : im (bit1 z) = bit0 (im z) := by
@@ -476,10 +449,7 @@ theorem real_smul_ofReal (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
 #align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofReal
 
 /- warning: is_R_or_C.of_real_mul_re -> IsROrC.ofReal_mul_re is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_reₓ'. -/
 @[is_R_or_C_simps]
 theorem ofReal_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
@@ -487,10 +457,7 @@ theorem ofReal_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
 #align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_re
 
 /- warning: is_R_or_C.of_real_mul_im -> IsROrC.ofReal_mul_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_mul_im IsROrC.ofReal_mul_imₓ'. -/
 @[is_R_or_C_simps]
 theorem ofReal_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
@@ -498,10 +465,7 @@ theorem ofReal_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
 #align is_R_or_C.of_real_mul_im IsROrC.ofReal_mul_im
 
 /- warning: is_R_or_C.smul_re -> IsROrC.smul_re is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.smul_re IsROrC.smul_reₓ'. -/
 @[is_R_or_C_simps]
 theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
@@ -509,10 +473,7 @@ theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
 #align is_R_or_C.smul_re IsROrC.smul_re
 
 /- warning: is_R_or_C.smul_im -> IsROrC.smul_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.smul_im IsROrC.smul_imₓ'. -/
 @[is_R_or_C_simps]
 theorem smul_im (r : ℝ) (z : K) : im (r • z) = r * im z := by
@@ -561,10 +522,7 @@ theorem I_re : re (i : K) = 0 :=
 #align is_R_or_C.I_re IsROrC.I_re
 
 /- warning: is_R_or_C.I_im -> IsROrC.I_im 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 is_R_or_C.I_im IsROrC.I_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem I_im (z : K) : im z * im (i : K) = im z :=
@@ -572,20 +530,14 @@ theorem I_im (z : K) : im z * im (i : K) = im z :=
 #align is_R_or_C.I_im IsROrC.I_im
 
 /- warning: is_R_or_C.I_im' -> IsROrC.I_im' 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 is_R_or_C.I_im' IsROrC.I_im'ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem I_im' (z : K) : im (i : K) * im z = im z := by rw [mul_comm, I_im _]
 #align is_R_or_C.I_im' IsROrC.I_im'
 
 /- warning: is_R_or_C.I_mul_re -> IsROrC.I_mul_re is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_mul_re IsROrC.I_mul_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem I_mul_re (z : K) : re (i * z) = -im z := by
@@ -603,10 +555,7 @@ theorem I_mul_I : (i : K) = 0 ∨ (i : K) * i = -1 :=
 #align is_R_or_C.I_mul_I IsROrC.I_mul_I
 
 /- warning: is_R_or_C.conj_re -> IsROrC.conj_re is a dubious translation:
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(Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_re IsROrC.conj_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_re (z : K) : re (conj z) = re z :=
@@ -614,10 +563,7 @@ theorem conj_re (z : K) : re (conj z) = re z :=
 #align is_R_or_C.conj_re IsROrC.conj_re
 
 /- warning: is_R_or_C.conj_im -> IsROrC.conj_im is a dubious translation:
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Neg.neg.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_im IsROrC.conj_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_im (z : K) : im (conj z) = -im z :=
@@ -649,10 +595,7 @@ theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) :=
 #align is_R_or_C.conj_of_real IsROrC.conj_ofReal
 
 /- warning: is_R_or_C.conj_bit0 -> IsROrC.conj_bit0 is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_bit0 IsROrC.conj_bit0ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
@@ -660,10 +603,7 @@ theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
 #align is_R_or_C.conj_bit0 IsROrC.conj_bit0
 
 /- warning: is_R_or_C.conj_bit1 -> IsROrC.conj_bit1 is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_bit1 IsROrC.conj_bit1ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
@@ -681,10 +621,7 @@ theorem conj_neg_I : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
 #align is_R_or_C.conj_neg_I IsROrC.conj_neg_I
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_imₓ'. -/
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
   (congr_arg conj (re_add_im z).symm).trans <| by
@@ -692,10 +629,7 @@ theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
 #align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_im
 
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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.sub_conj IsROrC.sub_conjₓ'. -/
 theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
   by
@@ -704,10 +638,7 @@ theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
 #align is_R_or_C.sub_conj IsROrC.sub_conj
 
 /- warning: is_R_or_C.conj_smul -> IsROrC.conj_smul is a dubious translation:
-lean 3 declaration is
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(RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
-but is expected to have type
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_inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (HSMul.hSMul.{0, u1, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (instHSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Algebra.toSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toSeminormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))) (IsROrC.toNormedAlgebra.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))) r (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_smul IsROrC.conj_smulₓ'. -/
 @[is_R_or_C_simps]
 theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
@@ -716,10 +647,7 @@ theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
 #align is_R_or_C.conj_smul IsROrC.conj_smul
 
 /- warning: is_R_or_C.add_conj -> IsROrC.add_conj is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} 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(AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.add_conj IsROrC.add_conjₓ'. -/
 theorem add_conj (z : K) : z + conj z = 2 * re z :=
   calc
@@ -729,20 +657,14 @@ theorem add_conj (z : K) : z + conj z = 2 * re z :=
 #align is_R_or_C.add_conj IsROrC.add_conj
 
 /- warning: is_R_or_C.re_eq_add_conj -> IsROrC.re_eq_add_conj is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
-but is expected to have type
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conjₓ'. -/
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
   rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
 #align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
 
 /- warning: is_R_or_C.im_eq_conj_sub -> IsROrC.im_eq_conj_sub is a dubious translation:
-lean 3 declaration is
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) 2 (instOfNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) 2 (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_subₓ'. -/
 theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
   rw [← neg_inj, ← of_real_neg, ← I_mul_re, re_eq_add_conj, map_mul, conj_I, ← neg_div, ← mul_neg,
@@ -750,10 +672,7 @@ theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
 #align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_sub
 
 /- warning: is_R_or_C.is_real_tfae -> IsROrC.is_real_TFAE 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 is_R_or_C.is_real_tfae IsROrC.is_real_TFAEₓ'. -/
 /-- There are several equivalent ways to say that a number `z` is in fact a real number. -/
 theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] :=
@@ -781,20 +700,14 @@ theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
 #align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_real
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_reₓ'. -/
 theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
   (is_real_TFAE z).out 0 2
 #align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_imₓ'. -/
 theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
   (is_real_TFAE z).out 0 3
@@ -840,20 +753,14 @@ def normSq : K →*₀ ℝ where
 -/
 
 /- warning: is_R_or_C.norm_sq_apply -> IsROrC.normSq_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_apply IsROrC.normSq_applyₓ'. -/
 theorem normSq_apply (z : K) : normSq z = re z * re z + im z * im z :=
   rfl
 #align is_R_or_C.norm_sq_apply IsROrC.normSq_apply
 
 /- warning: is_R_or_C.norm_sq_eq_def -> IsROrC.norm_sq_eq_def 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 is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_defₓ'. -/
 theorem norm_sq_eq_def {z : K} : ‖z‖ ^ 2 = re z * re z + im z * im z :=
   norm_sq_eq_def_ax z
@@ -926,20 +833,14 @@ theorem normSq_pos {z : K} : 0 < normSq z ↔ z ≠ 0 := by
 #align is_R_or_C.norm_sq_pos IsROrC.normSq_pos
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_neg IsROrC.normSq_negₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [norm_sq_eq_def', norm_neg]
 #align is_R_or_C.norm_sq_neg IsROrC.normSq_neg
 
 /- warning: is_R_or_C.norm_sq_conj -> IsROrC.normSq_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.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun 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z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_conj IsROrC.normSq_conjₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
@@ -947,10 +848,7 @@ theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
 #align is_R_or_C.norm_sq_conj IsROrC.normSq_conj
 
 /- warning: is_R_or_C.norm_sq_mul -> IsROrC.normSq_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_mul IsROrC.normSq_mulₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
@@ -958,10 +856,7 @@ theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
 #align is_R_or_C.norm_sq_mul IsROrC.normSq_mul
 
 /- warning: is_R_or_C.norm_sq_add -> IsROrC.normSq_add is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_add IsROrC.normSq_addₓ'. -/
 theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) :=
   by
@@ -970,30 +865,21 @@ theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z
 #align is_R_or_C.norm_sq_add IsROrC.normSq_add
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
 #align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
 #align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
 
 /- warning: is_R_or_C.mul_conj -> IsROrC.mul_conj is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_conj IsROrC.mul_conjₓ'. -/
 theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
   simp only [map_add, add_zero, ext_iff, add_left_inj, mul_eq_mul_left_iff, MulZeroClass.zero_mul,
@@ -1003,19 +889,13 @@ theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
 #align is_R_or_C.mul_conj IsROrC.mul_conj
 
 /- warning: is_R_or_C.conj_mul -> IsROrC.conj_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_mul IsROrC.conj_mulₓ'. -/
 theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
 #align is_R_or_C.conj_mul IsROrC.conj_mul
 
 /- warning: is_R_or_C.norm_sq_sub -> IsROrC.normSq_sub is a dubious translation:
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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K 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(Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) w) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_sub IsROrC.normSq_subₓ'. -/
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [norm_sq_add, sub_eq_add_neg, RingEquiv.map_neg, mul_neg, norm_sq_neg, map_neg]
@@ -1061,10 +941,7 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
 #align is_R_or_C.inv_def IsROrC.inv_def
 
 /- warning: is_R_or_C.inv_re -> IsROrC.inv_re is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_re IsROrC.inv_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
@@ -1072,10 +949,7 @@ theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
 #align is_R_or_C.inv_re IsROrC.inv_re
 
 /- warning: is_R_or_C.inv_im -> IsROrC.inv_im is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_im IsROrC.inv_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
@@ -1083,10 +957,7 @@ theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
 #align is_R_or_C.inv_im IsROrC.inv_im
 
 /- warning: is_R_or_C.div_re -> IsROrC.div_re is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_re IsROrC.div_reₓ'. -/
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, neg_mul, mul_neg, neg_neg, map_neg,
@@ -1094,10 +965,7 @@ theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / n
 #align is_R_or_C.div_re IsROrC.div_re
 
 /- warning: is_R_or_C.div_im -> IsROrC.div_im is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_im IsROrC.div_imₓ'. -/
 theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm, neg_mul, mul_neg, map_neg,
@@ -1105,10 +973,7 @@ theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / n
 #align is_R_or_C.div_im IsROrC.div_im
 
 /- warning: is_R_or_C.conj_inv -> IsROrC.conj_inv is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_inv IsROrC.conj_invₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
@@ -1127,10 +992,7 @@ theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
 #align is_R_or_C.of_real_div IsROrC.ofReal_div
 
 /- warning: is_R_or_C.div_re_of_real -> IsROrC.div_re_ofReal is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_re_of_real IsROrC.div_re_ofRealₓ'. -/
 theorem div_re_ofReal {z : K} {r : ℝ} : re (z / r) = re z / r := by
   rw [div_eq_inv_mul, div_eq_inv_mul, ← of_real_inv, of_real_mul_re]
@@ -1177,10 +1039,7 @@ theorem div_I (z : K) : z / i = -(z * i) := by rw [div_eq_mul_inv, inv_I, mul_ne
 #align is_R_or_C.div_I IsROrC.div_I
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_inv IsROrC.normSq_invₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
@@ -1188,10 +1047,7 @@ theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
 #align is_R_or_C.norm_sq_inv IsROrC.normSq_inv
 
 /- warning: is_R_or_C.norm_sq_div -> IsROrC.normSq_div is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_div IsROrC.normSq_divₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
@@ -1419,10 +1275,7 @@ theorem im_le_norm (z : K) : im z ≤ ‖z‖ :=
 #align is_R_or_C.im_le_norm IsROrC.im_le_norm
 
 /- warning: is_R_or_C.im_eq_zero_of_le -> IsROrC.im_eq_zero_of_le is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_leₓ'. -/
 theorem im_eq_zero_of_le {a : K} (h : ‖a‖ ≤ re a) : im a = 0 := by
   simpa only [mul_self_norm a, norm_sq_apply, self_eq_add_right, mul_self_eq_zero] using
@@ -1430,10 +1283,7 @@ theorem im_eq_zero_of_le {a : K} (h : ‖a‖ ≤ re a) : im a = 0 := by
 #align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_le
 
 /- warning: is_R_or_C.re_eq_self_of_le -> IsROrC.re_eq_self_of_le is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_leₓ'. -/
 theorem re_eq_self_of_le {a : K} (h : ‖a‖ ≤ re a) : (re a : K) = a := by
   rw [(is_real_tfae a).out 2 3, im_eq_zero_of_le h]
@@ -1442,10 +1292,7 @@ theorem re_eq_self_of_le {a : K} (h : ‖a‖ ≤ re a) : (re a : K) = a := by
 open IsAbsoluteValue
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_oneₓ'. -/
 theorem abs_re_div_norm_le_one (z : K) : |re z / ‖z‖| ≤ 1 :=
   by
@@ -1454,10 +1301,7 @@ theorem abs_re_div_norm_le_one (z : K) : |re z / ‖z‖| ≤ 1 :=
 #align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_one
 
 /- warning: is_R_or_C.abs_im_div_norm_le_one -> IsROrC.abs_im_div_norm_le_one is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_oneₓ'. -/
 theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
   by
@@ -1466,20 +1310,14 @@ theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
 #align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conjₓ'. -/
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, of_real_re, norm_of_real, abs_of_nonneg (norm_sq_nonneg _)]
 #align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj
 
 /- warning: is_R_or_C.norm_sq_re_add_conj -> IsROrC.norm_sq_re_add_conj is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Nat Real (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Real.instMonoidReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conjₓ'. -/
 theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
   rw [add_conj, norm_mul, norm_two, norm_of_real, two_mul (re x : K), map_add, of_real_re, ←
@@ -1487,10 +1325,7 @@ theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2
 #align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conj
 
 /- warning: is_R_or_C.norm_sq_re_conj_add -> IsROrC.norm_sq_re_conj_add is a dubious translation:
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(NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Nat Real (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Real.instMonoidReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) 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(IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_addₓ'. -/
 theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2 := by
   rw [add_comm, norm_sq_re_add_conj]
@@ -1679,10 +1514,7 @@ def reLm : K →ₗ[ℝ] ℝ :=
 -/
 
 /- warning: is_R_or_C.re_lm_coe -> IsROrC.reLm_coe is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_lm_coe IsROrC.reLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem reLm_coe : (reLm : K → ℝ) = re :=
@@ -1706,10 +1538,7 @@ theorem reClm_coe : ((reClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
 -/
 
 /- warning: is_R_or_C.re_clm_apply -> IsROrC.reClm_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_clm_apply IsROrC.reClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem reClm_apply : ((reClm : K →L[ℝ] ℝ) : K → ℝ) = re :=
@@ -1735,10 +1564,7 @@ def imLm : K →ₗ[ℝ] ℝ :=
 -/
 
 /- warning: is_R_or_C.im_lm_coe -> IsROrC.imLm_coe is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_lm_coe IsROrC.imLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem imLm_coe : (imLm : K → ℝ) = im :=
@@ -1762,10 +1588,7 @@ theorem imClm_coe : ((imClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
 -/
 
 /- warning: is_R_or_C.im_clm_apply -> IsROrC.imClm_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_clm_apply IsROrC.imClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem imClm_apply : ((imClm : K →L[ℝ] ℝ) : K → ℝ) = im :=
@@ -1795,10 +1618,7 @@ def conjAe : K ≃ₐ[ℝ] K :=
 -/
 
 /- warning: is_R_or_C.conj_ae_coe -> IsROrC.conjAe_coe is a dubious translation:
-lean 3 declaration is
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : K) => K) _x) (SMulHomClass.toFunLike.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K 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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (AlgEquivClass.toAlgHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K 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(NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))))) (IsROrC.conjAe.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K 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(NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_ae_coe IsROrC.conjAe_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjAe_coe : (conjAe : K → K) = conj :=
@@ -1813,10 +1633,7 @@ noncomputable def conjLie : K ≃ₗᵢ[ℝ] K :=
 -/
 
 /- warning: is_R_or_C.conj_lie_apply -> IsROrC.conjLie_apply is a dubious translation:
-lean 3 declaration is
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(IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => K -> K) 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(NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.conjLie.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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-but is expected to have type
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(NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) 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_inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, u1, u1, u1} Real Real K K (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{0, 0, u1, u1, u1} Real Real K K (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{0, 0, u1, u1} Real Real K K 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.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))))) (IsROrC.conjLie.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_lie_apply IsROrC.conjLie_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjLie_apply : (conjLie : K → K) = conj :=
@@ -1838,10 +1655,7 @@ theorem conjCle_coe : (@conjCle K _).toLinearEquiv = conjAe.toLinearEquiv :=
 -/
 
 /- warning: is_R_or_C.conj_cle_apply -> IsROrC.conjCle_apply is a dubious translation:
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-but is expected to have type
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(NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, 0, 0, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_cle_apply IsROrC.conjCle_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjCle_apply : (conjCle : K → K) = conj :=
@@ -1886,10 +1700,7 @@ noncomputable def ofRealLi : ℝ →ₗᵢ[ℝ] K
 -/
 
 /- warning: is_R_or_C.of_real_li_apply -> IsROrC.ofRealLi_apply is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : Real), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => K) a) (FunLike.coe.{succ u1, 1, succ u1} (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => K) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real K (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, 0, u1} (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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 (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))))) (AddCommGroup.toAddCommMonoid.{0} Real (SeminormedAddCommGroup.toAddCommGroup.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, u1, u1} Real Real Real K (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{0, 0, 0, u1} Real Real Real K Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (IsROrC.ofRealLi.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_li_apply IsROrC.ofRealLi_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem ofRealLi_apply : (ofRealLi : ℝ → K) = coe :=
@@ -1911,10 +1722,7 @@ theorem ofRealClm_coe : (@ofRealClm K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinear
 -/
 
 /- warning: is_R_or_C.of_real_clm_apply -> IsROrC.ofRealClm_apply is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => Real -> K) (IsROrC.ofRealClm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (fun (_x : ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => Real -> K) (ContinuousLinearMap.toFun.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.ofRealClm.{u1} K _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : Real), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => K) a) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => K) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real K (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, 0, u1} (ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))) (IsROrC.ofRealClm.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_clm_apply IsROrC.ofRealClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem ofRealClm_apply : (ofRealClm : ℝ → K) = coe :=

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

@@ -1682,7 +1682,7 @@ def reLm : K →ₗ[ℝ] ℝ :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (IsROrC.reLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) (fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (LinearMap.hasCoeToFun.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.reLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.reLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.reLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_lm_coe IsROrC.reLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem reLm_coe : (reLm : K → ℝ) = re :=
@@ -1738,7 +1738,7 @@ def imLm : K →ₗ[ℝ] ℝ :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (IsROrC.imLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) (fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (LinearMap.hasCoeToFun.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.imLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.imLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.imLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_lm_coe IsROrC.imLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem imLm_coe : (imLm : K → ℝ) = im :=
@@ -1798,7 +1798,7 @@ def conjAe : K ≃ₐ[ℝ] K :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : AlgEquiv.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) => K -> K) (IsROrC.conjAe.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (fun (_x : AlgEquiv.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) => K -> K) (AlgEquiv.hasCoeToFun.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (IsROrC.conjAe.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => K) _x) (SMulHomClass.toFunLike.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{0, u1, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (AlgEquivClass.toAlgHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))))) (IsROrC.conjAe.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : K) => K) _x) (SMulHomClass.toFunLike.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{0, u1, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (AlgEquivClass.toAlgHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))))) (IsROrC.conjAe.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_ae_coe IsROrC.conjAe_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjAe_coe : (conjAe : K → K) = conj :=

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

@@ -137,7 +137,7 @@ theorem real_smul_eq_coe_smul [AddCommGroup E] [Module K E] [Module ℝ E] [IsSc
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (Real -> K) (coeFn.{succ u1, succ u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => Real -> K) (RingHom.hasCoeToFun.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (algebraMap.{0, u1} Real K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (ᾰ : Real), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => K) ᾰ) (FunLike.coe.{succ u1, 1, succ u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => K) _x) (MulHomClass.toFunLike.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (algebraMap.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.ofReal.{u1} K _inst_1)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (ᾰ : Real), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => K) ᾰ) (FunLike.coe.{succ u1, 1, succ u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => K) _x) (MulHomClass.toFunLike.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (algebraMap.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.ofReal.{u1} K _inst_1)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_ofRealₓ'. -/
 theorem algebraMap_eq_ofReal : ⇑(algebraMap ℝ K) = coe :=
   rfl
@@ -606,7 +606,7 @@ theorem I_mul_I : (i : K) = 0 ∨ (i : K) * i = -1 :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_re IsROrC.conj_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_re (z : K) : re (conj z) = re z :=
@@ -617,7 +617,7 @@ theorem conj_re (z : K) : re (conj z) = re z :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Neg.neg.{0} Real Real.hasNeg (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Neg.neg.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Neg.neg.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_im IsROrC.conj_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_im (z : K) : im (conj z) = -im z :=
@@ -628,7 +628,7 @@ theorem conj_im (z : K) : im (conj z) = -im z :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.i.{u1} K _inst_1)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (IsROrC.i.{u1} K _inst_1))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.I.{u1} K _inst_1)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) _inst_1)))))) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) _inst_1))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.I.{u1} K _inst_1)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) _inst_1)))))) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.I.{u1} K _inst_1)) _inst_1))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_I IsROrC.conj_Iₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_I : conj (i : K) = -i :=
@@ -639,7 +639,7 @@ theorem conj_I : conj (i : K) = -i :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.ofReal.{u1} K _inst_1 r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1 r)) (IsROrC.ofReal.{u1} K _inst_1 r)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (IsROrC.ofReal.{u1} K _inst_1 r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1 r)) (IsROrC.ofReal.{u1} K _inst_1 r)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_of_real IsROrC.conj_ofRealₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) :=
@@ -652,7 +652,7 @@ theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_bit0 IsROrC.conj_bit0ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
@@ -663,7 +663,7 @@ theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_bit1 IsROrC.conj_bit1ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
@@ -674,7 +674,7 @@ theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (IsROrC.i.{u1} K _inst_1))) (IsROrC.i.{u1} K _inst_1)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.I.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.I.{u1} K _inst_1))) (IsROrC.I.{u1} K _inst_1)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.I.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.I.{u1} K _inst_1))) (IsROrC.I.{u1} K _inst_1)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_neg_I IsROrC.conj_neg_Iₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_neg_I : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
@@ -684,7 +684,7 @@ theorem conj_neg_I : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (IsROrC.i.{u1} K _inst_1)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))) (IsROrC.ofReal.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))) (IsROrC.ofReal.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))) (IsROrC.ofReal.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))) (IsROrC.ofReal.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_imₓ'. -/
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
   (congr_arg conj (re_add_im z).symm).trans <| by
@@ -695,7 +695,7 @@ theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z))) (IsROrC.i.{u1} K _inst_1))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HSub.hSub.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))) (IsROrC.I.{u1} K _inst_1))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HSub.hSub.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))) (IsROrC.I.{u1} K _inst_1))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.sub_conj IsROrC.sub_conjₓ'. -/
 theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
   by
@@ -707,7 +707,7 @@ theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) r z)) (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) r (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (HSMul.hSMul.{0, u1, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Algebra.toSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toSeminormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))) (IsROrC.toNormedAlgebra.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))) r (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (HSMul.hSMul.{0, u1, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (instHSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Algebra.toSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toSeminormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))) (IsROrC.toNormedAlgebra.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))) r (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_smul IsROrC.conj_smulₓ'. -/
 @[is_R_or_C_simps]
 theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
@@ -719,7 +719,7 @@ theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.add_conj IsROrC.add_conjₓ'. -/
 theorem add_conj (z : K) : z + conj z = 2 * re z :=
   calc
@@ -732,7 +732,7 @@ theorem add_conj (z : K) : z + conj z = 2 * re z :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conjₓ'. -/
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
   rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
@@ -742,7 +742,7 @@ theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (IsROrC.i.{u1} K _inst_1) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z)) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.ofReal.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) 2 (instOfNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) 2 (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.ofReal.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) 2 (instOfNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) 2 (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_subₓ'. -/
 theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
   rw [← neg_inj, ← of_real_neg, ← I_mul_re, re_eq_add_conj, map_mul, conj_I, ← neg_div, ← mul_neg,
@@ -753,7 +753,7 @@ theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), List.TFAE (List.cons.{0} Prop (Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (List.cons.{0} Prop (Exists.{1} Real (fun (r : Real) => Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) z)) (List.cons.{0} Prop (Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) z) (List.cons.{0} Prop (Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (List.nil.{0} Prop)))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), List.TFAE (List.cons.{0} Prop (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (List.cons.{0} Prop (Exists.{1} Real (fun (r : Real) => Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 r) z)) (List.cons.{0} Prop (Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) z) (List.cons.{0} Prop (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instZeroReal))) (List.nil.{0} Prop)))))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), List.TFAE (List.cons.{0} Prop (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (List.cons.{0} Prop (Exists.{1} Real (fun (r : Real) => Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 r) z)) (List.cons.{0} Prop (Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) z) (List.cons.{0} Prop (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instZeroReal))) (List.nil.{0} Prop)))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_real_tfae IsROrC.is_real_TFAEₓ'. -/
 /-- There are several equivalent ways to say that a number `z` is in fact a real number. -/
 theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] :=
@@ -774,7 +774,7 @@ theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(r
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{succ u1} K z ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{succ u1} K z (IsROrC.ofReal.{u1} K _inst_1 r)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{succ u1} K z (IsROrC.ofReal.{u1} K _inst_1 r)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_realₓ'. -/
 theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
   ((is_real_TFAE z).out 0 1).trans <| by simp only [eq_comm]
@@ -784,7 +784,7 @@ theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_reₓ'. -/
 theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
   (is_real_TFAE z).out 0 2
@@ -794,7 +794,7 @@ theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instZeroReal)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_imₓ'. -/
 theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
   (is_real_TFAE z).out 0 3
@@ -804,7 +804,7 @@ theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (K -> K) (Star.star.{u1} K (InvolutiveStar.toHasStar.{u1} K (StarAddMonoid.toHasInvolutiveStar.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalSemiring.{u1} K (NonUnitalNormedRing.toNonUnitalRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (StarRing.toStarAddMonoid.{u1} K (NonUnitalRing.toNonUnitalSemiring.{u1} K (NonUnitalNormedRing.toNonUnitalRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (IsROrC.toStarRing.{u1} K _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (K -> K) (Star.star.{u1} K (InvolutiveStar.toStar.{u1} K (StarAddMonoid.toInvolutiveStar.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (Ring.toAddGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (StarRing.toStarAddMonoid.{u1} K (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} K (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (IsROrC.toStarRing.{u1} K _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (K -> K) (Star.star.{u1} K (InvolutiveStar.toStar.{u1} K (StarAddMonoid.toInvolutiveStar.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (Ring.toAddGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (StarRing.toStarAddMonoid.{u1} K (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} K (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (IsROrC.toStarRing.{u1} K _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.star_def IsROrC.star_defₓ'. -/
 @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
@@ -843,7 +843,7 @@ def normSq : K →*₀ ℝ where
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instAddReal) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K 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 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_apply IsROrC.normSq_applyₓ'. -/
 theorem normSq_apply (z : K) : normSq z = re z * re z + im z * im z :=
   rfl
@@ -863,7 +863,7 @@ theorem norm_sq_eq_def {z : K} : ‖z‖ ^ 2 = re z * re z + im z * im z :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'ₓ'. -/
 theorem normSq_eq_def' (z : K) : normSq z = ‖z‖ ^ 2 :=
   norm_sq_eq_def.symm
@@ -873,7 +873,7 @@ theorem normSq_eq_def' (z : K) : normSq z = ‖z‖ ^ 2 :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instZeroReal))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instZeroReal))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_zero IsROrC.normSq_zeroₓ'. -/
 @[is_R_or_C_simps]
 theorem normSq_zero : normSq (0 : K) = 0 :=
@@ -884,7 +884,7 @@ theorem normSq_zero : normSq (0 : K) = 0 :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instOneReal))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_one IsROrC.normSq_oneₓ'. -/
 @[is_R_or_C_simps]
 theorem normSq_one : normSq (1 : K) = 1 :=
@@ -895,7 +895,7 @@ theorem normSq_one : normSq (1 : K) = 1 :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instZeroReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instZeroReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonnegₓ'. -/
 theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
@@ -905,7 +905,7 @@ theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{succ u1} K z (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instZeroReal))) (Eq.{succ u1} K z (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instZeroReal))) (Eq.{succ u1} K z (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zeroₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 :=
@@ -918,7 +918,7 @@ theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)) (Ne.{succ u1} K z (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instZeroReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)) (Ne.{succ u1} K z (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instZeroReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)) (Ne.{succ u1} K z (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_pos IsROrC.normSq_posₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_pos {z : K} : 0 < normSq z ↔ z ≠ 0 := by
@@ -929,7 +929,7 @@ theorem normSq_pos {z : K} : 0 < normSq z ↔ z ≠ 0 := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_neg IsROrC.normSq_negₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [norm_sq_eq_def', norm_neg]
@@ -939,7 +939,7 @@ theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [norm_sq_eq_
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_conj IsROrC.normSq_conjₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
@@ -950,7 +950,7 @@ theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_mul IsROrC.normSq_mulₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
@@ -961,7 +961,7 @@ theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w)) (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)))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHAdd.{0} ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) w) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instAddReal) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) 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_inst_1))))))))))) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) w) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_add IsROrC.normSq_addₓ'. -/
 theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) :=
   by
@@ -973,7 +973,7 @@ theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
@@ -983,7 +983,7 @@ theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
@@ -993,7 +993,7 @@ theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_conj IsROrC.mul_conjₓ'. -/
 theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
   simp only [map_add, add_zero, ext_iff, add_left_inj, mul_eq_mul_left_iff, MulZeroClass.zero_mul,
@@ -1006,7 +1006,7 @@ theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) x))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) x))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) x))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_mul IsROrC.conj_mulₓ'. -/
 theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
 #align is_R_or_C.conj_mul IsROrC.conj_mul
@@ -1015,7 +1015,7 @@ theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_c
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w)) (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)))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instAddReal) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real 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K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) w) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instAddReal) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_sub IsROrC.normSq_subₓ'. -/
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [norm_sq_add, sub_eq_add_neg, RingEquiv.map_neg, mul_neg, norm_sq_neg, map_neg]
@@ -1025,7 +1025,7 @@ theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Real.sqrt (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Real.sqrt (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Real.sqrt (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_normₓ'. -/
 theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
   rw [norm_sq_eq_def', Real.sqrt_sq (norm_nonneg _)]
@@ -1049,7 +1049,7 @@ theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = r⁻¹ :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (Inv.inv.{0} Real Real.hasInv (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) (IsROrC.ofReal.{u1} K _inst_1 (Inv.inv.{0} Real Real.instInvReal (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) (IsROrC.ofReal.{u1} K _inst_1 (Inv.inv.{0} Real Real.instInvReal (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_def IsROrC.inv_defₓ'. -/
 theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
   by
@@ -1064,7 +1064,7 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_re IsROrC.inv_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
@@ -1075,7 +1075,7 @@ theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Neg.neg.{0} Real Real.hasNeg (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (Neg.neg.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (Neg.neg.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_im IsROrC.inv_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
@@ -1086,7 +1086,7 @@ theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
 lean 3 declaration is
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_inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HDiv.hDiv.{0, 0, 0} Real Real Real 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0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instAddReal) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instAddReal) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K 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(AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) 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_inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_re IsROrC.div_reₓ'. -/
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, neg_mul, mul_neg, neg_neg, map_neg,
@@ -1097,7 +1097,7 @@ theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / n
 lean 3 declaration is
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_inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K 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(AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) w)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHSub.{0} ((fun 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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K 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(MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instSubReal) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K 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(AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) 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_inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_im IsROrC.div_imₓ'. -/
 theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm, neg_mul, mul_neg, map_neg,
@@ -1108,7 +1108,7 @@ theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / n
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) x)) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) x)) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) x)) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_inv IsROrC.conj_invₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
@@ -1180,7 +1180,7 @@ theorem div_I (z : K) : z / i = -(z * i) := by rw [div_eq_mul_inv, inv_I, mul_ne
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (Inv.inv.{0} Real Real.hasInv (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instInvReal (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instInvReal (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_inv IsROrC.normSq_invₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
@@ -1191,7 +1191,7 @@ theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_div IsROrC.normSq_divₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
@@ -1202,7 +1202,7 @@ theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (NormedField.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) z) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_conj IsROrC.norm_conjₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_norm_sq_eq_norm, norm_sq_conj]
@@ -1337,7 +1337,7 @@ theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_self_norm IsROrC.mul_self_normₓ'. -/
 theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [norm_sq_eq_def', sq]
 #align is_R_or_C.mul_self_norm IsROrC.mul_self_norm
@@ -1469,7 +1469,7 @@ theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conjₓ'. -/
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, of_real_re, norm_of_real, abs_of_nonneg (norm_sq_nonneg _)]
@@ -1479,7 +1479,7 @@ theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := b
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (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)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Nat Real (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Real.instMonoidReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Nat Real (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Real.instMonoidReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conjₓ'. -/
 theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
   rw [add_conj, norm_mul, norm_two, norm_of_real, two_mul (re x : K), map_add, of_real_re, ←
@@ -1490,7 +1490,7 @@ theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (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)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Nat Real (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Real.instMonoidReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Nat Real (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Real.instMonoidReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_addₓ'. -/
 theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2 := by
   rw [add_comm, norm_sq_re_add_conj]
@@ -1632,7 +1632,7 @@ theorem im_to_real {x : ℝ} : imR x = 0 :=
 lean 3 declaration is
   forall {x : Real}, Eq.{1} Real (coeFn.{1, 1} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (fun (_x : RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) => Real -> Real) (RingHom.hasCoeToFun.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (starRingEnd.{0} Real Real.commSemiring Real.starRing) x) x
 but is expected to have type
-  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (RingHom.instRingHomClassRingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))))) (starRingEnd.{0} Real Real.instCommSemiringReal Real.instStarRingRealToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x) x
+  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (RingHom.instRingHomClassRingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))))) (starRingEnd.{0} Real Real.instCommSemiringReal Real.instStarRingRealToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x) x
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_to_real IsROrC.conj_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_to_real {x : ℝ} : conj x = x :=
@@ -1654,7 +1654,7 @@ theorem I_to_real : IR = 0 :=
 lean 3 declaration is
   forall {x : Real}, Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Real -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{0} Real Real.isROrC) x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x x)
 but is expected to have type
-  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (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} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{0} Real Real.isROrC) x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x)
+  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (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} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{0} Real Real.isROrC) x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x)
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [IsROrC.normSq]
@@ -1798,7 +1798,7 @@ def conjAe : K ≃ₐ[ℝ] K :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : AlgEquiv.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) => K -> K) (IsROrC.conjAe.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (fun (_x : AlgEquiv.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) => K -> K) (AlgEquiv.hasCoeToFun.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (IsROrC.conjAe.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => K) _x) (SMulHomClass.toFunLike.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{0, u1, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (AlgEquivClass.toAlgHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))))) (IsROrC.conjAe.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => K) _x) (SMulHomClass.toFunLike.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{0, u1, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (AlgEquivClass.toAlgHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))))) (IsROrC.conjAe.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_ae_coe IsROrC.conjAe_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjAe_coe : (conjAe : K → K) = conj :=
@@ -1816,7 +1816,7 @@ noncomputable def conjLie : K ≃ₗᵢ[ℝ] K :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => K -> K) (IsROrC.conjLie.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (fun (_x : LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => K -> K) (LinearIsometryEquiv.hasCoeToFun.{0, 0, u1, u1} Real Real K K 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.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.conjLie.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, u1, u1, u1} Real Real K K (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{0, 0, u1, u1, u1} Real Real K K (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{0, 0, u1, u1} Real Real K K 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.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))))) (IsROrC.conjLie.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, u1, u1, u1} Real Real K K (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{0, 0, u1, u1, u1} Real Real K K (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{0, 0, u1, u1} Real Real K K 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.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))))) (IsROrC.conjLie.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_lie_apply IsROrC.conjLie_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjLie_apply : (conjLie : K → K) = conj :=
@@ -1841,7 +1841,7 @@ theorem conjCle_coe : (@conjCle K _).toLinearEquiv = conjAe.toLinearEquiv :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => K -> K) (IsROrC.conjCle.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (fun (_x : ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => K -> K) (ContinuousLinearEquiv.hasCoeToFun.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.conjCle.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, 0, 0, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (IsROrC.conjCle.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, 0, 0, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (IsROrC.conjCle.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_cle_apply IsROrC.conjCle_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjCle_apply : (conjCle : K → K) = conj :=
@@ -1855,7 +1855,7 @@ instance (priority := 100) : ContinuousStar K :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, u1} K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, u1} K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, u1} K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_conj IsROrC.continuous_conjₓ'. -/
 @[continuity]
 theorem continuous_conj : Continuous (conj : K → K) :=
@@ -1932,7 +1932,7 @@ theorem continuous_ofReal : Continuous (coe : ℝ → K) :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_norm_sq IsROrC.continuous_normSqₓ'. -/
 @[continuity]
 theorem continuous_normSq : Continuous (normSq : K → ℝ) :=

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

@@ -1682,7 +1682,7 @@ def reLm : K →ₗ[ℝ] ℝ :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (IsROrC.reLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) (fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (LinearMap.hasCoeToFun.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.reLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.reLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.reLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_lm_coe IsROrC.reLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem reLm_coe : (reLm : K → ℝ) = re :=
@@ -1738,7 +1738,7 @@ def imLm : K →ₗ[ℝ] ℝ :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (IsROrC.imLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) (fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (LinearMap.hasCoeToFun.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.imLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.imLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1))
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.imLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1))
 Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_lm_coe IsROrC.imLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem imLm_coe : (imLm : K → ℝ) = im :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
+! leanprover-community/mathlib commit 6cf5900728239efa287df7761ec2a1ac9cf39b29
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.NormedSpace.ContinuousLinearMap
 /-!
 # `is_R_or_C`: a typeclass for ℝ or ℂ
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the typeclass `is_R_or_C` intended to have only two instances:
 ℝ and ℂ. It is meant for definitions and theorems which hold for both the real and the complex case,
 and in particular when the real case follows directly from the complex case by setting `re` to `id`,

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

@@ -52,6 +52,7 @@ local notation "𝓚" => algebraMap ℝ _
 
 open ComplexConjugate
 
+#print IsROrC /-
 /--
 This typeclass captures properties shared by ℝ and ℂ, with an API that closely matches that of ℂ.
 -/
@@ -74,6 +75,7 @@ class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebr
   norm_sq_eq_def_ax : ∀ z : K, ‖z‖ ^ 2 = re z * re z + im z * im z
   mul_im_i_ax : ∀ z : K, im z * im I = im z
 #align is_R_or_C IsROrC
+-/
 
 end
 
@@ -90,298 +92,632 @@ namespace IsROrC
 
 open ComplexConjugate
 
+/- warning: is_R_or_C.algebra_map_coe -> IsROrC.algebraMapCoe is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], CoeTCₓ.{1, succ u1} Real K
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], CoeTC.{1, succ u1} Real K
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.algebra_map_coe IsROrC.algebraMapCoeₓ'. -/
 /- The priority must be set at 900 to ensure that coercions are tried in the right order.
 See Note [coercion into rings], or `data/nat/cast.lean` for more details. -/
 noncomputable instance (priority := 900) algebraMapCoe : CoeTC ℝ K :=
   ⟨algebraMap ℝ K⟩
 #align is_R_or_C.algebra_map_coe IsROrC.algebraMapCoe
 
-theorem of_real_alg (x : ℝ) : (x : K) = x • (1 : K) :=
+/- warning: is_R_or_C.of_real_alg -> IsROrC.ofReal_alg is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) x) (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) x (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 x) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) x (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_alg IsROrC.ofReal_algₓ'. -/
+theorem ofReal_alg (x : ℝ) : (x : K) = x • (1 : K) :=
   Algebra.algebraMap_eq_smul_one x
-#align is_R_or_C.of_real_alg IsROrC.of_real_alg
-
+#align is_R_or_C.of_real_alg IsROrC.ofReal_alg
+
+/- warning: is_R_or_C.real_smul_eq_coe_mul -> IsROrC.real_smul_eq_coe_mul is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{succ u1} K (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) r z) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{succ u1} K (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.real_smul_eq_coe_mul IsROrC.real_smul_eq_coe_mulₓ'. -/
 theorem real_smul_eq_coe_mul (r : ℝ) (z : K) : r • z = (r : K) * z :=
   Algebra.smul_def r z
 #align is_R_or_C.real_smul_eq_coe_mul IsROrC.real_smul_eq_coe_mul
 
+#print IsROrC.real_smul_eq_coe_smul /-
 theorem real_smul_eq_coe_smul [AddCommGroup E] [Module K E] [Module ℝ E] [IsScalarTower ℝ K E]
-    (r : ℝ) (x : E) : r • x = (r : K) • x := by rw [IsROrC.of_real_alg, smul_one_smul]
+    (r : ℝ) (x : E) : r • x = (r : K) • x := by rw [IsROrC.ofReal_alg, smul_one_smul]
 #align is_R_or_C.real_smul_eq_coe_smul IsROrC.real_smul_eq_coe_smul
+-/
 
-theorem algebraMap_eq_of_real : ⇑(algebraMap ℝ K) = coe :=
+/- warning: is_R_or_C.algebra_map_eq_of_real -> IsROrC.algebraMap_eq_ofReal is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (Real -> K) (coeFn.{succ u1, succ u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => Real -> K) (RingHom.hasCoeToFun.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (algebraMap.{0, u1} Real K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (ᾰ : Real), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => K) ᾰ) (FunLike.coe.{succ u1, 1, succ u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => K) _x) (MulHomClass.toFunLike.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, 0, u1} (RingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{0, u1} Real K (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (algebraMap.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.ofReal.{u1} K _inst_1)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_ofRealₓ'. -/
+theorem algebraMap_eq_ofReal : ⇑(algebraMap ℝ K) = coe :=
   rfl
-#align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_of_real
-
+#align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_ofReal
+
+/- warning: is_R_or_C.re_add_im -> IsROrC.re_add_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (IsROrC.i.{u1} K _inst_1))) z
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K 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(Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K 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(AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (IsROrC.I.{u1} K _inst_1))) z
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_add_im IsROrC.re_add_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem re_add_im (z : K) : (re z : K) + im z * i = z :=
   IsROrC.re_add_im_ax z
 #align is_R_or_C.re_add_im IsROrC.re_add_im
 
+/- warning: is_R_or_C.of_real_re -> IsROrC.ofReal_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)) r
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.ofReal.{u1} K _inst_1 r)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (IsROrC.ofReal.{u1} K _inst_1 r)) r
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_re IsROrC.ofReal_reₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_re : ∀ r : ℝ, re (r : K) = r :=
+theorem ofReal_re : ∀ r : ℝ, re (r : K) = r :=
   IsROrC.of_real_re_ax
-#align is_R_or_C.of_real_re IsROrC.of_real_re
-
+#align is_R_or_C.of_real_re IsROrC.ofReal_re
+
+/- warning: is_R_or_C.of_real_im -> IsROrC.ofReal_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.ofReal.{u1} K _inst_1 r)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (IsROrC.ofReal.{u1} K _inst_1 r)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.ofReal.{u1} K _inst_1 r)) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.ofReal.{u1} K _inst_1 r)) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_im IsROrC.ofReal_imₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_im : ∀ r : ℝ, im (r : K) = 0 :=
+theorem ofReal_im : ∀ r : ℝ, im (r : K) = 0 :=
   IsROrC.of_real_im_ax
-#align is_R_or_C.of_real_im IsROrC.of_real_im
-
+#align is_R_or_C.of_real_im IsROrC.ofReal_im
+
+/- warning: is_R_or_C.mul_re -> IsROrC.mul_re is a dubious translation:
+lean 3 declaration is
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_inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HMul.hMul.{0, 0, 0} Real Real Real 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_re IsROrC.mul_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem mul_re : ∀ z w : K, re (z * w) = re z * re w - im z * im w :=
   IsROrC.mul_re_ax
 #align is_R_or_C.mul_re IsROrC.mul_re
 
+/- warning: is_R_or_C.mul_im -> IsROrC.mul_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K 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(instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K 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(NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) w)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instAddReal) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_im IsROrC.mul_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
   IsROrC.mul_im_ax
 #align is_R_or_C.mul_im IsROrC.mul_im
 
+/- warning: is_R_or_C.ext_iff -> IsROrC.ext_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) w)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.ext_iff IsROrC.ext_iffₓ'. -/
 theorem ext_iff {z w : K} : z = w ↔ re z = re w ∧ im z = im w :=
   ⟨fun h => h ▸ ⟨rfl, rfl⟩, fun ⟨h₁, h₂⟩ => re_add_im z ▸ re_add_im w ▸ h₁ ▸ h₂ ▸ rfl⟩
 #align is_R_or_C.ext_iff IsROrC.ext_iff
 
+/- warning: is_R_or_C.ext -> IsROrC.ext is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.ext IsROrC.extₓ'. -/
 theorem ext {z w : K} (hre : re z = re w) (him : im z = im w) : z = w :=
   ext_iff.2 ⟨hre, him⟩
 #align is_R_or_C.ext IsROrC.ext
 
+/- warning: is_R_or_C.of_real_zero -> IsROrC.ofReal_zero is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_zero IsROrC.ofReal_zeroₓ'. -/
 @[norm_cast]
-theorem of_real_zero : ((0 : ℝ) : K) = 0 :=
+theorem ofReal_zero : ((0 : ℝ) : K) = 0 :=
   algebraMap.coe_zero
-#align is_R_or_C.of_real_zero IsROrC.of_real_zero
-
+#align is_R_or_C.of_real_zero IsROrC.ofReal_zero
+
+/- warning: is_R_or_C.zero_re' -> IsROrC.zero_re' is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.zero_re' IsROrC.zero_re'ₓ'. -/
 @[is_R_or_C_simps]
 theorem zero_re' : re (0 : K) = (0 : ℝ) :=
   map_zero re
 #align is_R_or_C.zero_re' IsROrC.zero_re'
 
+/- warning: is_R_or_C.of_real_one -> IsROrC.ofReal_one is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_one IsROrC.ofReal_oneₓ'. -/
 @[norm_cast]
-theorem of_real_one : ((1 : ℝ) : K) = 1 :=
+theorem ofReal_one : ((1 : ℝ) : K) = 1 :=
   map_one (algebraMap ℝ K)
-#align is_R_or_C.of_real_one IsROrC.of_real_one
-
+#align is_R_or_C.of_real_one IsROrC.ofReal_one
+
+/- warning: is_R_or_C.one_re -> IsROrC.one_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.one_re IsROrC.one_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem one_re : re (1 : K) = 1 := by rw [← of_real_one, of_real_re]
 #align is_R_or_C.one_re IsROrC.one_re
 
+/- warning: is_R_or_C.one_im -> IsROrC.one_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.one_im IsROrC.one_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem one_im : im (1 : K) = 0 := by rw [← of_real_one, of_real_im]
 #align is_R_or_C.one_im IsROrC.one_im
 
-theorem of_real_injective : Function.Injective (coe : ℝ → K) :=
+#print IsROrC.ofReal_injective /-
+theorem ofReal_injective : Function.Injective (coe : ℝ → K) :=
   (algebraMap ℝ K).Injective
-#align is_R_or_C.of_real_injective IsROrC.of_real_injective
+#align is_R_or_C.of_real_injective IsROrC.ofReal_injective
+-/
 
+#print IsROrC.ofReal_inj /-
 @[norm_cast]
-theorem of_real_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
+theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
   algebraMap.coe_inj
-#align is_R_or_C.of_real_inj IsROrC.of_real_inj
+#align is_R_or_C.of_real_inj IsROrC.ofReal_inj
+-/
 
+/- warning: is_R_or_C.bit0_re -> IsROrC.bit0_re is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit0_re IsROrC.bit0_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_re IsROrC.bit0_re
 
+/- warning: is_R_or_C.bit1_re -> IsROrC.bit1_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit1.{0} Real Real.hasOne Real.hasAdd (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K 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(AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instOneReal Real.instAddReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit1_re IsROrC.bit1_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_add, bit0_re, one_re]
 #align is_R_or_C.bit1_re IsROrC.bit1_re
 
+/- warning: is_R_or_C.bit0_im -> IsROrC.bit0_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit0.{0} Real Real.hasAdd (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instAddReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit0_im IsROrC.bit0_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_im IsROrC.bit0_im
 
+/- warning: is_R_or_C.bit1_im -> IsROrC.bit1_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit0.{0} Real Real.hasAdd (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instAddReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.bit1_im IsROrC.bit1_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem bit1_im (z : K) : im (bit1 z) = bit0 (im z) := by
   simp only [bit1, map_add, bit0_im, one_im, add_zero]
 #align is_R_or_C.bit1_im IsROrC.bit1_im
 
-theorem of_real_eq_zero {x : ℝ} : (x : K) = 0 ↔ x = 0 :=
+/- warning: is_R_or_C.of_real_eq_zero -> IsROrC.ofReal_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {x : Real}, Iff (Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {x : Real}, Iff (Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 x) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_eq_zero IsROrC.ofReal_eq_zeroₓ'. -/
+theorem ofReal_eq_zero {x : ℝ} : (x : K) = 0 ↔ x = 0 :=
   algebraMap.lift_map_eq_zero_iff x
-#align is_R_or_C.of_real_eq_zero IsROrC.of_real_eq_zero
-
-theorem of_real_ne_zero {x : ℝ} : (x : K) ≠ 0 ↔ x ≠ 0 :=
-  of_real_eq_zero.Not
-#align is_R_or_C.of_real_ne_zero IsROrC.of_real_ne_zero
-
+#align is_R_or_C.of_real_eq_zero IsROrC.ofReal_eq_zero
+
+/- warning: is_R_or_C.of_real_ne_zero -> IsROrC.ofReal_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {x : Real}, Iff (Ne.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {x : Real}, Iff (Ne.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 x) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_ne_zero IsROrC.ofReal_ne_zeroₓ'. -/
+theorem ofReal_ne_zero {x : ℝ} : (x : K) ≠ 0 ↔ x ≠ 0 :=
+  ofReal_eq_zero.Not
+#align is_R_or_C.of_real_ne_zero IsROrC.ofReal_ne_zero
+
+/- warning: is_R_or_C.of_real_add -> IsROrC.ofReal_add is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (s : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r s)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) s))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (s : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r s)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) (IsROrC.ofReal.{u1} K _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_add IsROrC.ofReal_addₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_add (r s : ℝ) : ((r + s : ℝ) : K) = r + s :=
+theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : K) = r + s :=
   algebraMap.coe_add _ _
-#align is_R_or_C.of_real_add IsROrC.of_real_add
-
+#align is_R_or_C.of_real_add IsROrC.ofReal_add
+
+/- warning: is_R_or_C.of_real_bit0 -> IsROrC.ofReal_bit0 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (bit0.{0} Real Real.hasAdd r)) (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (bit0.{0} Real Real.instAddReal r)) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (IsROrC.ofReal.{u1} K _inst_1 r))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_bit0 IsROrC.ofReal_bit0ₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
-  of_real_add _ _
-#align is_R_or_C.of_real_bit0 IsROrC.of_real_bit0
-
+theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
+  ofReal_add _ _
+#align is_R_or_C.of_real_bit0 IsROrC.ofReal_bit0
+
+/- warning: is_R_or_C.of_real_bit1 -> IsROrC.ofReal_bit1 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (bit1.{0} Real Real.hasOne Real.hasAdd r)) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (bit1.{0} Real Real.instOneReal Real.instAddReal r)) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (IsROrC.ofReal.{u1} K _inst_1 r))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_bit1 IsROrC.ofReal_bit1ₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
+theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
   map_bit1 (algebraMap ℝ K) r
-#align is_R_or_C.of_real_bit1 IsROrC.of_real_bit1
-
+#align is_R_or_C.of_real_bit1 IsROrC.ofReal_bit1
+
+/- warning: is_R_or_C.of_real_neg -> IsROrC.ofReal_neg is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (Neg.neg.{0} Real Real.hasNeg r)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (Neg.neg.{0} Real Real.instNegReal r)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.ofReal.{u1} K _inst_1 r))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_neg IsROrC.ofReal_negₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_neg (r : ℝ) : ((-r : ℝ) : K) = -r :=
+theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : K) = -r :=
   algebraMap.coe_neg r
-#align is_R_or_C.of_real_neg IsROrC.of_real_neg
-
+#align is_R_or_C.of_real_neg IsROrC.ofReal_neg
+
+/- warning: is_R_or_C.of_real_sub -> IsROrC.ofReal_sub is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (s : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) r s)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) s))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (s : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) r s)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (IsROrC.ofReal.{u1} K _inst_1 r) (IsROrC.ofReal.{u1} K _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_sub IsROrC.ofReal_subₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
+theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
   map_sub (algebraMap ℝ K) r s
-#align is_R_or_C.of_real_sub IsROrC.of_real_sub
+#align is_R_or_C.of_real_sub IsROrC.ofReal_sub
 
+#print IsROrC.ofReal_sum /-
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_sum {α : Type _} (s : Finset α) (f : α → ℝ) :
+theorem ofReal_sum {α : Type _} (s : Finset α) (f : α → ℝ) :
     ((∑ i in s, f i : ℝ) : K) = ∑ i in s, (f i : K) :=
   map_sum (algebraMap ℝ K) _ _
-#align is_R_or_C.of_real_sum IsROrC.of_real_sum
+#align is_R_or_C.of_real_sum IsROrC.ofReal_sum
+-/
 
+/- warning: is_R_or_C.of_real_finsupp_sum -> IsROrC.ofReal_finsupp_sum is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {α : Type.{u2}} {M : Type.{u3}} [_inst_2 : Zero.{u3} M] (f : Finsupp.{u2, u3} α M _inst_2) (g : α -> M -> Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (Finsupp.sum.{u2, u3, 0} α M Real _inst_2 Real.addCommMonoid f (fun (a : α) (b : M) => g a b))) (Finsupp.sum.{u2, u3, u1} α M K _inst_2 (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) f (fun (a : α) (b : M) => (fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (g a b)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {α : Type.{u3}} {M : Type.{u2}} [_inst_2 : Zero.{u2} M] (f : Finsupp.{u3, u2} α M _inst_2) (g : α -> M -> Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (Finsupp.sum.{u3, u2, 0} α M Real _inst_2 Real.instAddCommMonoidReal f (fun (a : α) (b : M) => g a b))) (Finsupp.sum.{u3, u2, u1} α M K _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) f (fun (a : α) (b : M) => IsROrC.ofReal.{u1} K _inst_1 (g a b)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_finsupp_sum IsROrC.ofReal_finsupp_sumₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_finsupp_sum {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
+theorem ofReal_finsupp_sum {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.Sum fun a b => g a b : ℝ) : K) = f.Sum fun a b => (g a b : K) :=
   map_finsupp_sum (algebraMap ℝ K) f g
-#align is_R_or_C.of_real_finsupp_sum IsROrC.of_real_finsupp_sum
-
+#align is_R_or_C.of_real_finsupp_sum IsROrC.ofReal_finsupp_sum
+
+/- warning: is_R_or_C.of_real_mul -> IsROrC.ofReal_mul is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (s : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r s)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) s))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (s : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r s)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) (IsROrC.ofReal.{u1} K _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_mul IsROrC.ofReal_mulₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_mul (r s : ℝ) : ((r * s : ℝ) : K) = r * s :=
+theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : K) = r * s :=
   algebraMap.coe_mul _ _
-#align is_R_or_C.of_real_mul IsROrC.of_real_mul
-
+#align is_R_or_C.of_real_mul IsROrC.ofReal_mul
+
+/- warning: is_R_or_C.of_real_pow -> IsROrC.ofReal_pow is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (n : Nat), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) n)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (n : Nat), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) n)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_pow IsROrC.ofReal_powₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
+theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
   map_pow (algebraMap ℝ K) r n
-#align is_R_or_C.of_real_pow IsROrC.of_real_pow
+#align is_R_or_C.of_real_pow IsROrC.ofReal_pow
 
+#print IsROrC.ofReal_prod /-
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
+theorem ofReal_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
     ((∏ i in s, f i : ℝ) : K) = ∏ i in s, (f i : K) :=
   RingHom.map_prod _ _ _
-#align is_R_or_C.of_real_prod IsROrC.of_real_prod
+#align is_R_or_C.of_real_prod IsROrC.ofReal_prod
+-/
 
+/- warning: is_R_or_C.of_real_finsupp_prod -> IsROrC.ofReal_finsupp_prod is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {α : Type.{u2}} {M : Type.{u3}} [_inst_2 : Zero.{u3} M] (f : Finsupp.{u2, u3} α M _inst_2) (g : α -> M -> Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (Finsupp.prod.{u2, u3, 0} α M Real _inst_2 Real.commMonoid f (fun (a : α) (b : M) => g a b))) (Finsupp.prod.{u2, u3, u1} α M K _inst_2 (CommRing.toCommMonoid.{u1} K (SeminormedCommRing.toCommRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) f (fun (a : α) (b : M) => (fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (g a b)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {α : Type.{u3}} {M : Type.{u2}} [_inst_2 : Zero.{u2} M] (f : Finsupp.{u3, u2} α M _inst_2) (g : α -> M -> Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (Finsupp.prod.{u3, u2, 0} α M Real _inst_2 Real.instCommMonoidReal f (fun (a : α) (b : M) => g a b))) (Finsupp.prod.{u3, u2, u1} α M K _inst_2 (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) f (fun (a : α) (b : M) => IsROrC.ofReal.{u1} K _inst_1 (g a b)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_finsupp_prod IsROrC.ofReal_finsupp_prodₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
+theorem ofReal_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.Prod fun a b => g a b : ℝ) : K) = f.Prod fun a b => (g a b : K) :=
   RingHom.map_finsupp_prod _ f g
-#align is_R_or_C.of_real_finsupp_prod IsROrC.of_real_finsupp_prod
-
+#align is_R_or_C.of_real_finsupp_prod IsROrC.ofReal_finsupp_prod
+
+/- warning: is_R_or_C.real_smul_of_real -> IsROrC.real_smul_ofReal is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (x : Real), Eq.{succ u1} K (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) r ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) x)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) x))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (x : Real), Eq.{succ u1} K (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r (IsROrC.ofReal.{u1} K _inst_1 x)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) (IsROrC.ofReal.{u1} K _inst_1 x))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofRealₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem real_smul_of_real (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
+theorem real_smul_ofReal (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
   real_smul_eq_coe_mul _ _
-#align is_R_or_C.real_smul_of_real IsROrC.real_smul_of_real
-
+#align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofReal
+
+/- warning: is_R_or_C.of_real_mul_re -> IsROrC.ofReal_mul_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K 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(NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) z)) (HMul.hMul.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real (instHMul.{0} Real Real.instMulReal) r (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_reₓ'. -/
 @[is_R_or_C_simps]
-theorem of_real_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
+theorem ofReal_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
   simp only [mul_re, of_real_im, MulZeroClass.zero_mul, of_real_re, sub_zero]
-#align is_R_or_C.of_real_mul_re IsROrC.of_real_mul_re
-
+#align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_re
+
+/- warning: is_R_or_C.of_real_mul_im -> IsROrC.ofReal_mul_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.ofReal.{u1} K _inst_1 r) z)) (HMul.hMul.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real (instHMul.{0} Real Real.instMulReal) r (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_mul_im IsROrC.ofReal_mul_imₓ'. -/
 @[is_R_or_C_simps]
-theorem of_real_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
+theorem ofReal_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
   simp only [add_zero, of_real_im, MulZeroClass.zero_mul, of_real_re, mul_im]
-#align is_R_or_C.of_real_mul_im IsROrC.of_real_mul_im
-
+#align is_R_or_C.of_real_mul_im IsROrC.ofReal_mul_im
+
+/- warning: is_R_or_C.smul_re -> IsROrC.smul_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) r z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K 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(AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (HMul.hMul.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real (instHMul.{0} Real Real.instMulReal) r (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.smul_re IsROrC.smul_reₓ'. -/
 @[is_R_or_C_simps]
 theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
   rw [real_smul_eq_coe_mul, of_real_mul_re]
 #align is_R_or_C.smul_re IsROrC.smul_re
 
+/- warning: is_R_or_C.smul_im -> IsROrC.smul_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) r z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (HMul.hMul.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real (instHMul.{0} Real Real.instMulReal) r (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.smul_im IsROrC.smul_imₓ'. -/
 @[is_R_or_C_simps]
 theorem smul_im (r : ℝ) (z : K) : im (r • z) = r * im z := by
   rw [real_smul_eq_coe_mul, of_real_mul_im]
 #align is_R_or_C.smul_im IsROrC.smul_im
 
+/- warning: is_R_or_C.norm_of_real -> IsROrC.norm_ofReal is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{1} Real (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{1} Real (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (IsROrC.ofReal.{u1} K _inst_1 r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_of_real IsROrC.norm_ofRealₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem norm_of_real (r : ℝ) : ‖(r : K)‖ = |r| :=
+theorem norm_ofReal (r : ℝ) : ‖(r : K)‖ = |r| :=
   norm_algebraMap' K r
-#align is_R_or_C.norm_of_real IsROrC.norm_of_real
+#align is_R_or_C.norm_of_real IsROrC.norm_ofReal
 
 /-! ### Characteristic zero -/
 
 
+/- warning: is_R_or_C.char_zero_R_or_C -> IsROrC.charZero_isROrC is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], CharZero.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], CharZero.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (Ring.toAddGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.char_zero_R_or_C IsROrC.charZero_isROrCₓ'. -/
 -- see Note [lower instance priority]
 /-- ℝ and ℂ are both of characteristic zero.  -/
-instance (priority := 100) charZero_R_or_C : CharZero K :=
+instance (priority := 100) charZero_isROrC : CharZero K :=
   (RingHom.charZero_iff (algebraMap ℝ K).Injective).1 inferInstance
-#align is_R_or_C.char_zero_R_or_C IsROrC.charZero_R_or_C
+#align is_R_or_C.char_zero_R_or_C IsROrC.charZero_isROrC
 
 /-! ### The imaginary unit, `I` -/
 
 
+/- warning: is_R_or_C.I_re -> IsROrC.I_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (IsROrC.i.{u1} K _inst_1)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.I.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (IsROrC.I.{u1} K _inst_1)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.I.{u1} K _inst_1)) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.I.{u1} K _inst_1)) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_re IsROrC.I_reₓ'. -/
 /-- The imaginary unit. -/
 @[simp, is_R_or_C_simps]
-theorem i_re : re (i : K) = 0 :=
+theorem I_re : re (i : K) = 0 :=
   i_re_ax
-#align is_R_or_C.I_re IsROrC.i_re
-
+#align is_R_or_C.I_re IsROrC.I_re
+
+/- warning: is_R_or_C.I_im -> IsROrC.I_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (IsROrC.i.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.I.{u1} K _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K (fun 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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (IsROrC.I.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K 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(NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_im IsROrC.I_imₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem i_im (z : K) : im z * im (i : K) = im z :=
+theorem I_im (z : K) : im z * im (i : K) = im z :=
   mul_im_i_ax z
-#align is_R_or_C.I_im IsROrC.i_im
-
+#align is_R_or_C.I_im IsROrC.I_im
+
+/- warning: is_R_or_C.I_im' -> IsROrC.I_im' is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (IsROrC.i.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.I.{u1} K _inst_1)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.I.{u1} K _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.I.{u1} K _inst_1)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (IsROrC.I.{u1} K _inst_1)) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K 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(IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_im' IsROrC.I_im'ₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem i_im' (z : K) : im (i : K) * im z = im z := by rw [mul_comm, I_im _]
-#align is_R_or_C.I_im' IsROrC.i_im'
-
+theorem I_im' (z : K) : im (i : K) * im z = im z := by rw [mul_comm, I_im _]
+#align is_R_or_C.I_im' IsROrC.I_im'
+
+/- warning: is_R_or_C.I_mul_re -> IsROrC.I_mul_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (IsROrC.i.{u1} K _inst_1) z)) (Neg.neg.{0} Real Real.hasNeg (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.I.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K 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(NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.I.{u1} K _inst_1) z)) (Neg.neg.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_mul_re IsROrC.I_mul_reₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem i_mul_re (z : K) : re (i * z) = -im z := by
+theorem I_mul_re (z : K) : re (i * z) = -im z := by
   simp only [I_re, zero_sub, I_im', MulZeroClass.zero_mul, mul_re]
-#align is_R_or_C.I_mul_re IsROrC.i_mul_re
-
-theorem i_mul_i : (i : K) = 0 ∨ (i : K) * i = -1 :=
+#align is_R_or_C.I_mul_re IsROrC.I_mul_re
+
+/- warning: is_R_or_C.I_mul_I -> IsROrC.I_mul_I is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Or (Eq.{succ u1} K (IsROrC.i.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))) (Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (IsROrC.i.{u1} K _inst_1) (IsROrC.i.{u1} K _inst_1)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Or (Eq.{succ u1} K (IsROrC.I.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.I.{u1} K _inst_1) (IsROrC.I.{u1} K _inst_1)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_mul_I IsROrC.I_mul_Iₓ'. -/
+theorem I_mul_I : (i : K) = 0 ∨ (i : K) * i = -1 :=
   i_mul_i_ax
-#align is_R_or_C.I_mul_I IsROrC.i_mul_i
-
+#align is_R_or_C.I_mul_I IsROrC.I_mul_I
+
+/- warning: is_R_or_C.conj_re -> IsROrC.conj_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) 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(Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K 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(Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_re IsROrC.conj_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_re (z : K) : re (conj z) = re z :=
   IsROrC.conj_re_ax z
 #align is_R_or_C.conj_re IsROrC.conj_re
 
+/- warning: is_R_or_C.conj_im -> IsROrC.conj_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Neg.neg.{0} Real Real.hasNeg (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Neg.neg.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_im IsROrC.conj_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_im (z : K) : im (conj z) = -im z :=
   IsROrC.conj_im_ax z
 #align is_R_or_C.conj_im IsROrC.conj_im
 
+/- warning: is_R_or_C.conj_I -> IsROrC.conj_I is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.i.{u1} K _inst_1)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (IsROrC.i.{u1} K _inst_1))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.I.{u1} K _inst_1)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (Ring.toNeg.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) _inst_1)))))) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.I.{u1} K _inst_1)) _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_I IsROrC.conj_Iₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem conj_i : conj (i : K) = -i :=
+theorem conj_I : conj (i : K) = -i :=
   IsROrC.conj_i_ax
-#align is_R_or_C.conj_I IsROrC.conj_i
-
+#align is_R_or_C.conj_I IsROrC.conj_I
+
+/- warning: is_R_or_C.conj_of_real -> IsROrC.conj_ofReal is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (IsROrC.ofReal.{u1} K _inst_1 r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1 r)) (IsROrC.ofReal.{u1} K _inst_1 r)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_of_real IsROrC.conj_ofRealₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem conj_of_real (r : ℝ) : conj (r : K) = (r : K) :=
+theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) :=
   by
   rw [ext_iff]
   simp only [of_real_im, conj_im, eq_self_iff_true, conj_re, and_self_iff, neg_zero]
-#align is_R_or_C.conj_of_real IsROrC.conj_of_real
-
+#align is_R_or_C.conj_of_real IsROrC.conj_ofReal
+
+/- warning: is_R_or_C.conj_bit0 -> IsROrC.conj_bit0 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit0.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_bit0 IsROrC.conj_bit0ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
   map_bit0 _ _
 #align is_R_or_C.conj_bit0 IsROrC.conj_bit0
 
+/- warning: is_R_or_C.conj_bit1 -> IsROrC.conj_bit1 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z)) (bit1.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+but is expected to have type
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (bit1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (bit1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_bit1 IsROrC.conj_bit1ₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
   map_bit1 _ _
 #align is_R_or_C.conj_bit1 IsROrC.conj_bit1
 
+/- warning: is_R_or_C.conj_neg_I -> IsROrC.conj_neg_I is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (IsROrC.i.{u1} K _inst_1))) (IsROrC.i.{u1} K _inst_1)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.I.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.I.{u1} K _inst_1))) (IsROrC.I.{u1} K _inst_1)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_neg_I IsROrC.conj_neg_Iₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem conj_neg_i : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
-#align is_R_or_C.conj_neg_I IsROrC.conj_neg_i
-
+theorem conj_neg_I : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
+#align is_R_or_C.conj_neg_I IsROrC.conj_neg_I
+
+/- warning: is_R_or_C.conj_eq_re_sub_im -> IsROrC.conj_eq_re_sub_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K 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(AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (IsROrC.i.{u1} K _inst_1)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_imₓ'. -/
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
   (congr_arg conj (re_add_im z).symm).trans <| by
     rw [map_add, map_mul, conj_I, conj_of_real, conj_of_real, mul_neg, sub_eq_add_neg]
 #align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_im
 
+/- warning: is_R_or_C.sub_conj -> IsROrC.sub_conj is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z))) (IsROrC.I.{u1} K _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.sub_conj IsROrC.sub_conjₓ'. -/
 theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
   by
   nth_rw 1 [← re_add_im z]
   rw [conj_eq_re_sub_im, add_sub_sub_cancel, ← two_mul, mul_assoc]
 #align is_R_or_C.sub_conj IsROrC.sub_conj
 
+/- warning: is_R_or_C.conj_smul -> IsROrC.conj_smul is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) r z)) (SMul.smul.{0, u1} Real K (SMulZeroClass.toHasSmul.{0, u1} Real K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real K (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real K (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real K (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) r (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (HSMul.hSMul.{0, u1, u1} Real K K (instHSMul.{0, u1} Real K (Algebra.toSMul.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) r z)) (HSMul.hSMul.{0, u1, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Algebra.toSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toSeminormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))) (IsROrC.toNormedAlgebra.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))) r (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_smul IsROrC.conj_smulₓ'. -/
 @[is_R_or_C_simps]
 theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
   rw [conj_eq_re_sub_im, conj_eq_re_sub_im, smul_re, smul_im, of_real_mul, of_real_mul,
     real_smul_eq_coe_mul, mul_sub, mul_assoc]
 #align is_R_or_C.conj_smul IsROrC.conj_smul
 
+/- warning: is_R_or_C.add_conj -> IsROrC.add_conj is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.add_conj IsROrC.add_conjₓ'. -/
 theorem add_conj (z : K) : z + conj z = 2 * re z :=
   calc
     z + conj z = re z + im z * i + (re z - im z * i) := by rw [re_add_im, conj_eq_re_sub_im]
@@ -389,17 +725,35 @@ theorem add_conj (z : K) : z + conj z = 2 * re z :=
     
 #align is_R_or_C.add_conj IsROrC.add_conj
 
+/- warning: is_R_or_C.re_eq_add_conj -> IsROrC.re_eq_add_conj is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K 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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conjₓ'. -/
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
   rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
 #align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
 
+/- warning: is_R_or_C.im_eq_conj_sub -> IsROrC.im_eq_conj_sub is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (IsROrC.i.{u1} K _inst_1) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z)) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.ofReal.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))) (IsROrC.I.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toSub.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) 2 (instOfNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) 2 (Semiring.toNatCast.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_subₓ'. -/
 theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
   rw [← neg_inj, ← of_real_neg, ← I_mul_re, re_eq_add_conj, map_mul, conj_I, ← neg_div, ← mul_neg,
     neg_sub, mul_sub, neg_mul, sub_eq_add_neg]
 #align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_sub
 
+/- warning: is_R_or_C.is_real_tfae -> IsROrC.is_real_TFAE is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), List.TFAE (List.cons.{0} Prop (Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (List.cons.{0} Prop (Exists.{1} Real (fun 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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), List.TFAE (List.cons.{0} Prop (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instZeroReal))) (List.nil.{0} Prop)))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_real_tfae IsROrC.is_real_TFAEₓ'. -/
 /-- There are several equivalent ways to say that a number `z` is in fact a real number. -/
-theorem is_real_tFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] :=
+theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] :=
   by
   tfae_have 1 → 4
   · intro h
@@ -411,20 +765,44 @@ theorem is_real_tFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(r
   tfae_have 3 → 2; exact fun h => ⟨_, h⟩
   tfae_have 2 → 1; exact fun ⟨r, hr⟩ => hr ▸ conj_of_real _
   tfae_finish
-#align is_R_or_C.is_real_tfae IsROrC.is_real_tFAE
-
+#align is_R_or_C.is_real_tfae IsROrC.is_real_TFAE
+
+/- warning: is_R_or_C.conj_eq_iff_real -> IsROrC.conj_eq_iff_real is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_realₓ'. -/
 theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
-  ((is_real_tFAE z).out 0 1).trans <| by simp only [eq_comm]
+  ((is_real_TFAE z).out 0 1).trans <| by simp only [eq_comm]
 #align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_real
 
+/- warning: is_R_or_C.conj_eq_iff_re -> IsROrC.conj_eq_iff_re is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_reₓ'. -/
 theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
-  (is_real_tFAE z).out 0 2
+  (is_real_TFAE z).out 0 2
 #align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
 
+/- warning: is_R_or_C.conj_eq_iff_im -> IsROrC.conj_eq_iff_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
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(IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) z) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K 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(AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_imₓ'. -/
 theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
-  (is_real_tFAE z).out 0 3
+  (is_real_TFAE z).out 0 3
 #align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_im
 
+/- warning: is_R_or_C.star_def -> IsROrC.star_def is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (K -> K) (Star.star.{u1} K (InvolutiveStar.toHasStar.{u1} K (StarAddMonoid.toHasInvolutiveStar.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalSemiring.{u1} K (NonUnitalNormedRing.toNonUnitalRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (StarRing.toStarAddMonoid.{u1} K (NonUnitalRing.toNonUnitalSemiring.{u1} K (NonUnitalNormedRing.toNonUnitalRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (IsROrC.toStarRing.{u1} K _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (K -> K) (Star.star.{u1} K (InvolutiveStar.toStar.{u1} K (StarAddMonoid.toInvolutiveStar.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (Ring.toAddGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (StarRing.toStarAddMonoid.{u1} K (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} K (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (IsROrC.toStarRing.{u1} K _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.star_def IsROrC.star_defₓ'. -/
 @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
   rfl
@@ -432,6 +810,12 @@ theorem star_def : (Star.star : K → K) = conj :=
 
 variable (K)
 
+/- warning: is_R_or_C.conj_to_ring_equiv -> IsROrC.conjToRingEquiv is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) [_inst_1 : IsROrC.{u1} K], RingEquiv.{u1, u1} K (MulOpposite.{u1} K) (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (MulOpposite.hasMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (MulOpposite.hasAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))
+but is expected to have type
+  forall (K : Type.{u1}) [_inst_1 : IsROrC.{u1} K], RingEquiv.{u1, u1} K (MulOpposite.{u1} K) (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (MulOpposite.mul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOpposite.add.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_to_ring_equiv IsROrC.conjToRingEquivₓ'. -/
 /-- Conjugation as a ring equivalence. This is used to convert the inner product into a
 sesquilinear product. -/
 abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
@@ -440,6 +824,7 @@ abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
 
 variable {K}
 
+#print IsROrC.normSq /-
 /-- The norm squared function. -/
 def normSq : K →*₀ ℝ where
   toFun z := re z * re z + im z * im z
@@ -449,33 +834,76 @@ def normSq : K →*₀ ℝ where
     simp only [mul_im, mul_re]
     ring
 #align is_R_or_C.norm_sq IsROrC.normSq
+-/
 
+/- warning: is_R_or_C.norm_sq_apply -> IsROrC.normSq_apply is a dubious translation:
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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instAddReal) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K 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(CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_apply IsROrC.normSq_applyₓ'. -/
 theorem normSq_apply (z : K) : normSq z = re z * re z + im z * im z :=
   rfl
 #align is_R_or_C.norm_sq_apply IsROrC.normSq_apply
 
+/- warning: is_R_or_C.norm_sq_eq_def -> IsROrC.norm_sq_eq_def is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_defₓ'. -/
 theorem norm_sq_eq_def {z : K} : ‖z‖ ^ 2 = re z * re z + im z * im z :=
   norm_sq_eq_def_ax z
 #align is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_def
 
+/- warning: is_R_or_C.norm_sq_eq_def' -> IsROrC.normSq_eq_def' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'ₓ'. -/
 theorem normSq_eq_def' (z : K) : normSq z = ‖z‖ ^ 2 :=
   norm_sq_eq_def.symm
 #align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'
 
+/- warning: is_R_or_C.norm_sq_zero -> IsROrC.normSq_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) 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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_zero IsROrC.normSq_zeroₓ'. -/
 @[is_R_or_C_simps]
 theorem normSq_zero : normSq (0 : K) = 0 :=
   normSq.map_zero
 #align is_R_or_C.norm_sq_zero IsROrC.normSq_zero
 
+/- warning: is_R_or_C.norm_sq_one -> IsROrC.normSq_one is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_one IsROrC.normSq_oneₓ'. -/
 @[is_R_or_C_simps]
 theorem normSq_one : normSq (1 : K) = 1 :=
   normSq.map_one
 #align is_R_or_C.norm_sq_one IsROrC.normSq_one
 
+/- warning: is_R_or_C.norm_sq_nonneg -> IsROrC.normSq_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instZeroReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonnegₓ'. -/
 theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
 #align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonneg
 
+/- warning: is_R_or_C.norm_sq_eq_zero -> IsROrC.normSq_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{succ u1} K z (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instZeroReal))) (Eq.{succ u1} K z (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zeroₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 :=
   by
@@ -483,39 +911,87 @@ theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 :=
   simp [sq]
 #align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zero
 
+/- warning: is_R_or_C.norm_sq_pos -> IsROrC.normSq_pos is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)) (Ne.{succ u1} K z (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instZeroReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)) (Ne.{succ u1} K z (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_pos IsROrC.normSq_posₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_pos {z : K} : 0 < normSq z ↔ z ≠ 0 := by
   rw [lt_iff_le_and_ne, Ne, eq_comm] <;> simp [norm_sq_nonneg]
 #align is_R_or_C.norm_sq_pos IsROrC.normSq_pos
 
+/- warning: is_R_or_C.norm_sq_neg -> IsROrC.normSq_neg is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_neg IsROrC.normSq_negₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [norm_sq_eq_def', norm_neg]
 #align is_R_or_C.norm_sq_neg IsROrC.normSq_neg
 
+/- warning: is_R_or_C.norm_sq_conj -> IsROrC.normSq_conj is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) Real (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_conj IsROrC.normSq_conjₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
   simp only [norm_sq_apply, neg_mul, mul_neg, neg_neg, is_R_or_C_simps]
 #align is_R_or_C.norm_sq_conj IsROrC.normSq_conj
 
+/- warning: is_R_or_C.norm_sq_mul -> IsROrC.normSq_mul is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_mul IsROrC.normSq_mulₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
 #align is_R_or_C.norm_sq_mul IsROrC.normSq_mul
 
+/- warning: is_R_or_C.norm_sq_add -> IsROrC.normSq_add is a dubious translation:
+lean 3 declaration is
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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instAddReal) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) w) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (FunLike.coe.{succ u1, succ 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(RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_add IsROrC.normSq_addₓ'. -/
 theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) :=
   by
   simp only [norm_sq_apply, map_add, mul_neg, sub_neg_eq_add, is_R_or_C_simps]
   ring
 #align is_R_or_C.norm_sq_add IsROrC.normSq_add
 
+/- warning: is_R_or_C.re_sq_le_norm_sq -> IsROrC.re_sq_le_normSq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
 #align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSq
 
+/- warning: is_R_or_C.im_sq_le_norm_sq -> IsROrC.im_sq_le_normSq is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instMulReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K (fun (_x 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0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K 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(MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
 #align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
 
+/- warning: is_R_or_C.mul_conj -> IsROrC.mul_conj is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_conj IsROrC.mul_conjₓ'. -/
 theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
   simp only [map_add, add_zero, ext_iff, add_left_inj, mul_eq_mul_left_iff, MulZeroClass.zero_mul,
     add_comm, true_or_iff, eq_self_iff_true, mul_neg, add_right_neg, zero_add, norm_sq_apply,
@@ -523,13 +999,31 @@ theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
     is_R_or_C_simps]
 #align is_R_or_C.mul_conj IsROrC.mul_conj
 
+/- warning: is_R_or_C.conj_mul -> IsROrC.conj_mul is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) x))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x) (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) x))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_mul IsROrC.conj_mulₓ'. -/
 theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
 #align is_R_or_C.conj_mul IsROrC.conj_mul
 
+/- warning: is_R_or_C.norm_sq_sub -> IsROrC.normSq_sub is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w)) (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)))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instAddReal) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real 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K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} 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(fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) w)))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_sub IsROrC.normSq_subₓ'. -/
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [norm_sq_add, sub_eq_add_neg, RingEquiv.map_neg, mul_neg, norm_sq_neg, map_neg]
 #align is_R_or_C.norm_sq_sub IsROrC.normSq_sub
 
+/- warning: is_R_or_C.sqrt_norm_sq_eq_norm -> IsROrC.sqrt_normSq_eq_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Real.sqrt (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Real.sqrt (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_normₓ'. -/
 theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
   rw [norm_sq_eq_def', Real.sqrt_sq (norm_nonneg _)]
 #align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_norm
@@ -537,11 +1031,23 @@ theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
 /-! ### Inversion -/
 
 
+/- warning: is_R_or_C.of_real_inv -> IsROrC.ofReal_inv is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (Inv.inv.{0} Real Real.hasInv r)) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (Inv.inv.{0} Real Real.instInvReal r)) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.ofReal.{u1} K _inst_1 r))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_inv IsROrC.ofReal_invₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = r⁻¹ :=
+theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = r⁻¹ :=
   map_inv₀ (algebraMap ℝ K) r
-#align is_R_or_C.of_real_inv IsROrC.of_real_inv
-
+#align is_R_or_C.of_real_inv IsROrC.ofReal_inv
+
+/- warning: is_R_or_C.inv_def -> IsROrC.inv_def is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (Inv.inv.{0} Real Real.hasInv (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z) (IsROrC.ofReal.{u1} K _inst_1 (Inv.inv.{0} Real Real.instInvReal (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_def IsROrC.inv_defₓ'. -/
 theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
   by
   rcases eq_or_ne z 0 with (rfl | h₀)
@@ -551,70 +1057,150 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
     rwa [of_real_ne_zero, Ne.def, norm_sq_eq_zero]
 #align is_R_or_C.inv_def IsROrC.inv_def
 
+/- warning: is_R_or_C.inv_re -> IsROrC.inv_re is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_re IsROrC.inv_reₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
   rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_re, conj_re, div_eq_inv_mul]
 #align is_R_or_C.inv_re IsROrC.inv_re
 
+/- warning: is_R_or_C.inv_im -> IsROrC.inv_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Neg.neg.{0} Real Real.hasNeg (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real 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(IsROrC.normSq.{u1} K _inst_1) z))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (Neg.neg.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K 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(AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_im IsROrC.inv_imₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
   rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_im, conj_im, div_eq_inv_mul]
 #align is_R_or_C.inv_im IsROrC.inv_im
 
+/- warning: is_R_or_C.div_re -> IsROrC.div_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HDiv.hDiv.{0, 0, 0} Real Real Real 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+but is expected to have type
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Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHAdd.{0} ((fun 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(AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_re IsROrC.div_reₓ'. -/
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, neg_mul, mul_neg, neg_neg, map_neg,
     is_R_or_C_simps]
 #align is_R_or_C.div_re IsROrC.div_re
 
+/- warning: is_R_or_C.div_im -> IsROrC.div_im is a dubious translation:
+lean 3 declaration is
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0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) w)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K 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(AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHSub.{0} ((fun 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_inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_im IsROrC.div_imₓ'. -/
 theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm, neg_mul, mul_neg, map_neg,
     is_R_or_C_simps]
 #align is_R_or_C.div_im IsROrC.div_im
 
+/- warning: is_R_or_C.conj_inv -> IsROrC.conj_inv is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} K (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) x)) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) x)) (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K 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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_inv IsROrC.conj_invₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align is_R_or_C.conj_inv IsROrC.conj_inv
 
+/- warning: is_R_or_C.of_real_div -> IsROrC.ofReal_div is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (s : Real), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) r s)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) s))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (r : Real) (s : Real), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) r s)) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.ofReal.{u1} K _inst_1 r) (IsROrC.ofReal.{u1} K _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_div IsROrC.ofReal_divₓ'. -/
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
+theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
   map_div₀ (algebraMap ℝ K) r s
-#align is_R_or_C.of_real_div IsROrC.of_real_div
-
-theorem div_re_of_real {z : K} {r : ℝ} : re (z / r) = re z / r := by
+#align is_R_or_C.of_real_div IsROrC.ofReal_div
+
+/- warning: is_R_or_C.div_re_of_real -> IsROrC.div_re_ofReal is a dubious translation:
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+but is expected to have type
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_inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z (IsROrC.ofReal.{u1} K _inst_1 r))) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K 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(AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) r)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_re_of_real IsROrC.div_re_ofRealₓ'. -/
+theorem div_re_ofReal {z : K} {r : ℝ} : re (z / r) = re z / r := by
   rw [div_eq_inv_mul, div_eq_inv_mul, ← of_real_inv, of_real_mul_re]
-#align is_R_or_C.div_re_of_real IsROrC.div_re_of_real
+#align is_R_or_C.div_re_of_real IsROrC.div_re_ofReal
 
+#print IsROrC.ofReal_zpow /-
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : K) = r ^ n :=
+theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : K) = r ^ n :=
   map_zpow₀ (algebraMap ℝ K) r n
-#align is_R_or_C.of_real_zpow IsROrC.of_real_zpow
+#align is_R_or_C.of_real_zpow IsROrC.ofReal_zpow
+-/
 
-theorem i_mul_i_of_nonzero : (i : K) ≠ 0 → (i : K) * i = -1 :=
+/- warning: is_R_or_C.I_mul_I_of_nonzero -> IsROrC.I_mul_I_of_nonzero is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], (Ne.{succ u1} K (IsROrC.i.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))) -> (Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (IsROrC.i.{u1} K _inst_1) (IsROrC.i.{u1} K _inst_1)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], (Ne.{succ u1} K (IsROrC.I.{u1} K _inst_1) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) -> (Eq.{succ u1} K (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (IsROrC.I.{u1} K _inst_1) (IsROrC.I.{u1} K _inst_1)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_mul_I_of_nonzero IsROrC.I_mul_I_of_nonzeroₓ'. -/
+theorem I_mul_I_of_nonzero : (i : K) ≠ 0 → (i : K) * i = -1 :=
   i_mul_i_ax.resolve_left
-#align is_R_or_C.I_mul_I_of_nonzero IsROrC.i_mul_i_of_nonzero
-
+#align is_R_or_C.I_mul_I_of_nonzero IsROrC.I_mul_I_of_nonzero
+
+/- warning: is_R_or_C.inv_I -> IsROrC.inv_I is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.i.{u1} K _inst_1)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (IsROrC.i.{u1} K _inst_1))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} K (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.I.{u1} K _inst_1)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (IsROrC.I.{u1} K _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.inv_I IsROrC.inv_Iₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem inv_i : (i : K)⁻¹ = -i := by
+theorem inv_I : (i : K)⁻¹ = -i := by
   by_cases h : (I : K) = 0
   · simp [h]
   · field_simp [I_mul_I_of_nonzero h]
-#align is_R_or_C.inv_I IsROrC.inv_i
-
+#align is_R_or_C.inv_I IsROrC.inv_I
+
+/- warning: is_R_or_C.div_I -> IsROrC.div_I is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (DivInvMonoid.toHasDiv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) z (IsROrC.i.{u1} K _inst_1)) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) z (IsROrC.i.{u1} K _inst_1)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{succ u1} K (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z (IsROrC.I.{u1} K _inst_1)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) z (IsROrC.I.{u1} K _inst_1)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.div_I IsROrC.div_Iₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem div_i (z : K) : z / i = -(z * i) := by rw [div_eq_mul_inv, inv_I, mul_neg]
-#align is_R_or_C.div_I IsROrC.div_i
-
+theorem div_I (z : K) : z / i = -(z * i) := by rw [div_eq_mul_inv, inv_I, mul_neg]
+#align is_R_or_C.div_I IsROrC.div_I
+
+/- warning: is_R_or_C.norm_sq_inv -> IsROrC.normSq_inv is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) z)) (Inv.inv.{0} Real Real.hasInv (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z))
+but is expected to have type
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(NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instInvReal (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun 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Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_inv IsROrC.normSq_invₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ (@normSq K _) z
 #align is_R_or_C.norm_sq_inv IsROrC.normSq_inv
 
+/- warning: is_R_or_C.norm_sq_div -> IsROrC.normSq_div is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real 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(DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real 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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K) (w : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) (HDiv.hDiv.{u1, u1, u1} K K K (instHDiv.{u1} K (Field.toDiv.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K 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(MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) w))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_div IsROrC.normSq_divₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ (@normSq K _) z w
 #align is_R_or_C.norm_sq_div IsROrC.normSq_div
 
+/- warning: is_R_or_C.norm_conj -> IsROrC.norm_conj is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {z : K}, Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (NormedField.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) z) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_conj IsROrC.norm_conjₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_norm_sq_eq_norm, norm_sq_conj]
 #align is_R_or_C.norm_conj IsROrC.norm_conj
@@ -625,128 +1211,284 @@ instance (priority := 100) : CstarRing K
 /-! ### Cast lemmas -/
 
 
+/- warning: is_R_or_C.of_real_nat_cast -> IsROrC.ofReal_natCast is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) ((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)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat K (HasLiftT.mk.{1, succ u1} Nat K (CoeTCₓ.coe.{1, succ u1} Nat K (Nat.castCoe.{u1} K (AddMonoidWithOne.toNatCast.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) n)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (Nat.cast.{0} Real Real.natCast n)) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_nat_cast IsROrC.ofReal_natCastₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_nat_cast (n : ℕ) : ((n : ℝ) : K) = n :=
+theorem ofReal_natCast (n : ℕ) : ((n : ℝ) : K) = n :=
   map_natCast (algebraMap ℝ K) n
-#align is_R_or_C.of_real_nat_cast IsROrC.of_real_nat_cast
-
+#align is_R_or_C.of_real_nat_cast IsROrC.ofReal_natCast
+
+/- warning: is_R_or_C.nat_cast_re -> IsROrC.natCast_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat K (HasLiftT.mk.{1, succ u1} Nat K (CoeTCₓ.coe.{1, succ u1} Nat K (Nat.castCoe.{u1} K (AddMonoidWithOne.toNatCast.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) 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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) Real.natCast n)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.nat_cast_re IsROrC.natCast_reₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem nat_cast_re (n : ℕ) : re (n : K) = n := by rw [← of_real_nat_cast, of_real_re]
-#align is_R_or_C.nat_cast_re IsROrC.nat_cast_re
-
+theorem natCast_re (n : ℕ) : re (n : K) = n := by rw [← of_real_nat_cast, of_real_re]
+#align is_R_or_C.nat_cast_re IsROrC.natCast_re
+
+/- warning: is_R_or_C.nat_cast_im -> IsROrC.natCast_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat K (HasLiftT.mk.{1, succ u1} Nat K (CoeTCₓ.coe.{1, succ u1} Nat K (Nat.castCoe.{u1} K (AddMonoidWithOne.toNatCast.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) n)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.nat_cast_im IsROrC.natCast_imₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem nat_cast_im (n : ℕ) : im (n : K) = 0 := by rw [← of_real_nat_cast, of_real_im]
-#align is_R_or_C.nat_cast_im IsROrC.nat_cast_im
-
+theorem natCast_im (n : ℕ) : im (n : K) = 0 := by rw [← of_real_nat_cast, of_real_im]
+#align is_R_or_C.nat_cast_im IsROrC.natCast_im
+
+/- warning: is_R_or_C.of_real_int_cast -> IsROrC.ofReal_intCast is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Int), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) ((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)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int K (HasLiftT.mk.{1, succ u1} Int K (CoeTCₓ.coe.{1, succ u1} Int K (Int.castCoe.{u1} K (AddGroupWithOne.toHasIntCast.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) n)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Int), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (Int.cast.{0} Real Real.intCast n)) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) n)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_int_cast IsROrC.ofReal_intCastₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_int_cast (n : ℤ) : ((n : ℝ) : K) = n :=
+theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : K) = n :=
   map_intCast (algebraMap ℝ K) n
-#align is_R_or_C.of_real_int_cast IsROrC.of_real_int_cast
-
+#align is_R_or_C.of_real_int_cast IsROrC.ofReal_intCast
+
+/- warning: is_R_or_C.int_cast_re -> IsROrC.intCast_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Int), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int K (HasLiftT.mk.{1, succ u1} Int K (CoeTCₓ.coe.{1, succ u1} Int K (Int.castCoe.{u1} K (AddGroupWithOne.toHasIntCast.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) 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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) n)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) n)) (Int.cast.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) n)) Real.intCast n)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.int_cast_re IsROrC.intCast_reₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem int_cast_re (n : ℤ) : re (n : K) = n := by rw [← of_real_int_cast, of_real_re]
-#align is_R_or_C.int_cast_re IsROrC.int_cast_re
-
+theorem intCast_re (n : ℤ) : re (n : K) = n := by rw [← of_real_int_cast, of_real_re]
+#align is_R_or_C.int_cast_re IsROrC.intCast_re
+
+/- warning: is_R_or_C.int_cast_im -> IsROrC.intCast_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Int), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int K (HasLiftT.mk.{1, succ u1} Int K (CoeTCₓ.coe.{1, succ u1} Int K (Int.castCoe.{u1} K (AddGroupWithOne.toHasIntCast.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) n)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) n)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) n)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) n)) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Int.cast.{u1} K (Ring.toIntCast.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) n)) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.int_cast_im IsROrC.intCast_imₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem int_cast_im (n : ℤ) : im (n : K) = 0 := by rw [← of_real_int_cast, of_real_im]
-#align is_R_or_C.int_cast_im IsROrC.int_cast_im
-
+theorem intCast_im (n : ℤ) : im (n : K) = 0 := by rw [← of_real_int_cast, of_real_im]
+#align is_R_or_C.int_cast_im IsROrC.intCast_im
+
+/- warning: is_R_or_C.of_real_rat_cast -> IsROrC.ofReal_ratCast is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Rat), Eq.{succ u1} K ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) ((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))) n)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat K (HasLiftT.mk.{1, succ u1} Rat K (CoeTCₓ.coe.{1, succ u1} Rat K (Rat.castCoe.{u1} K (DivisionRing.toHasRatCast.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) n)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Rat), Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (Rat.cast.{0} Real Real.ratCast n)) (Rat.cast.{u1} K (Field.toRatCast.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) n)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_rat_cast IsROrC.ofReal_ratCastₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_rat_cast (n : ℚ) : ((n : ℝ) : K) = n :=
+theorem ofReal_ratCast (n : ℚ) : ((n : ℝ) : K) = n :=
   map_ratCast (algebraMap ℝ K) n
-#align is_R_or_C.of_real_rat_cast IsROrC.of_real_rat_cast
-
+#align is_R_or_C.of_real_rat_cast IsROrC.ofReal_ratCast
+
+/- warning: is_R_or_C.rat_cast_re -> IsROrC.ratCast_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (q : Rat), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat K (HasLiftT.mk.{1, succ u1} Rat K (CoeTCₓ.coe.{1, succ u1} Rat K (Rat.castCoe.{u1} K (DivisionRing.toHasRatCast.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) q)) ((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))) q)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (q : Rat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Rat.cast.{u1} K (Field.toRatCast.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) q)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (Rat.cast.{u1} K (Field.toRatCast.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) q)) (Rat.cast.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Rat.cast.{u1} K (Field.toRatCast.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) q)) Real.ratCast q)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.rat_cast_re IsROrC.ratCast_reₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem rat_cast_re (q : ℚ) : re (q : K) = q := by rw [← of_real_rat_cast, of_real_re]
-#align is_R_or_C.rat_cast_re IsROrC.rat_cast_re
-
+theorem ratCast_re (q : ℚ) : re (q : K) = q := by rw [← of_real_rat_cast, of_real_re]
+#align is_R_or_C.rat_cast_re IsROrC.ratCast_re
+
+/- warning: is_R_or_C.rat_cast_im -> IsROrC.ratCast_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (q : Rat), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat K (HasLiftT.mk.{1, succ u1} Rat K (CoeTCₓ.coe.{1, succ u1} Rat K (Rat.castCoe.{u1} K (DivisionRing.toHasRatCast.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) q)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (q : Rat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Rat.cast.{u1} K (Field.toRatCast.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) q)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (Rat.cast.{u1} K (Field.toRatCast.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) q)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Rat.cast.{u1} K (Field.toRatCast.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) q)) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (Rat.cast.{u1} K (Field.toRatCast.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) q)) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.rat_cast_im IsROrC.ratCast_imₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem rat_cast_im (q : ℚ) : im (q : K) = 0 := by rw [← of_real_rat_cast, of_real_im]
-#align is_R_or_C.rat_cast_im IsROrC.rat_cast_im
+theorem ratCast_im (q : ℚ) : im (q : K) = 0 := by rw [← of_real_rat_cast, of_real_im]
+#align is_R_or_C.rat_cast_im IsROrC.ratCast_im
 
 /-! ### Norm -/
 
 
+/- warning: is_R_or_C.norm_of_nonneg -> IsROrC.norm_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{1} Real (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))) r)) r)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} Real (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (IsROrC.ofReal.{u1} K _inst_1 r)) r)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_of_nonneg IsROrC.norm_of_nonnegₓ'. -/
 theorem norm_of_nonneg {r : ℝ} (h : 0 ≤ r) : ‖(r : K)‖ = r :=
-  (norm_of_real _).trans (abs_of_nonneg h)
+  (norm_ofReal _).trans (abs_of_nonneg h)
 #align is_R_or_C.norm_of_nonneg IsROrC.norm_of_nonneg
 
+/- warning: is_R_or_C.norm_nat_cast -> IsROrC.norm_natCast is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{1} Real (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat K (HasLiftT.mk.{1, succ u1} Nat K (CoeTCₓ.coe.{1, succ u1} Nat K (Nat.castCoe.{u1} K (AddMonoidWithOne.toNatCast.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) 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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (n : Nat), Eq.{1} Real (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (Nat.cast.{u1} K (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) n)) (Nat.cast.{0} Real Real.natCast n)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_nat_cast IsROrC.norm_natCastₓ'. -/
 @[simp, is_R_or_C_simps, norm_cast]
-theorem norm_nat_cast (n : ℕ) : ‖(n : K)‖ = n :=
+theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n :=
   by
   rw [← of_real_nat_cast]
   exact norm_of_nonneg (Nat.cast_nonneg n)
-#align is_R_or_C.norm_nat_cast IsROrC.norm_nat_cast
-
+#align is_R_or_C.norm_nat_cast IsROrC.norm_natCast
+
+/- warning: is_R_or_C.mul_self_norm -> IsROrC.mul_self_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.mul_self_norm IsROrC.mul_self_normₓ'. -/
 theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [norm_sq_eq_def', sq]
 #align is_R_or_C.mul_self_norm IsROrC.mul_self_norm
 
 attribute [is_R_or_C_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
 
+/- warning: is_R_or_C.norm_two -> IsROrC.norm_two is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 2 (OfNat.mk.{u1} K 2 (bit0.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{1} Real (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 2 (instOfNat.{u1} K 2 (Semiring.toNatCast.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_two IsROrC.norm_twoₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem norm_two : ‖(2 : K)‖ = 2 := by rw [← Nat.cast_two, norm_nat_cast, Nat.cast_two]
 #align is_R_or_C.norm_two IsROrC.norm_two
 
+/- warning: is_R_or_C.abs_re_le_norm -> IsROrC.abs_re_le_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_re_le_norm IsROrC.abs_re_le_normₓ'. -/
 theorem abs_re_le_norm (z : K) : |re z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (re z)) (norm_nonneg _), abs_mul_abs_self,
       mul_self_norm] <;>
     apply re_sq_le_norm_sq
 #align is_R_or_C.abs_re_le_norm IsROrC.abs_re_le_norm
 
+/- warning: is_R_or_C.abs_im_le_norm -> IsROrC.abs_im_le_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_im_le_norm IsROrC.abs_im_le_normₓ'. -/
 theorem abs_im_le_norm (z : K) : |im z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (im z)) (norm_nonneg _), abs_mul_abs_self,
       mul_self_norm] <;>
     apply im_sq_le_norm_sq
 #align is_R_or_C.abs_im_le_norm IsROrC.abs_im_le_norm
 
+/- warning: is_R_or_C.norm_re_le_norm -> IsROrC.norm_re_le_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (Norm.norm.{0} Real Real.hasNorm (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.norm (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_re_le_norm IsROrC.norm_re_le_normₓ'. -/
 theorem norm_re_le_norm (z : K) : ‖re z‖ ≤ ‖z‖ :=
   abs_re_le_norm z
 #align is_R_or_C.norm_re_le_norm IsROrC.norm_re_le_norm
 
+/- warning: is_R_or_C.norm_im_le_norm -> IsROrC.norm_im_le_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (Norm.norm.{0} Real Real.hasNorm (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.norm (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_im_le_norm IsROrC.norm_im_le_normₓ'. -/
 theorem norm_im_le_norm (z : K) : ‖im z‖ ≤ ‖z‖ :=
   abs_im_le_norm z
 #align is_R_or_C.norm_im_le_norm IsROrC.norm_im_le_norm
 
+/- warning: is_R_or_C.re_le_norm -> IsROrC.re_le_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_le_norm IsROrC.re_le_normₓ'. -/
 theorem re_le_norm (z : K) : re z ≤ ‖z‖ :=
   (abs_le.1 (abs_re_le_norm z)).2
 #align is_R_or_C.re_le_norm IsROrC.re_le_norm
 
+/- warning: is_R_or_C.im_le_norm -> IsROrC.im_le_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_le_norm IsROrC.im_le_normₓ'. -/
 theorem im_le_norm (z : K) : im z ≤ ‖z‖ :=
   (abs_le.1 (abs_im_le_norm _)).2
 #align is_R_or_C.im_le_norm IsROrC.im_le_norm
 
+/- warning: is_R_or_C.im_eq_zero_of_le -> IsROrC.im_eq_zero_of_le is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {a : K}, (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) a) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) a)) -> (Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) a) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
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+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {a : K}, (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) a) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K 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(AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) a)) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K 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(Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) a) Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_leₓ'. -/
 theorem im_eq_zero_of_le {a : K} (h : ‖a‖ ≤ re a) : im a = 0 := by
   simpa only [mul_self_norm a, norm_sq_apply, self_eq_add_right, mul_self_eq_zero] using
     congr_arg (fun z => z * z) ((re_le_norm a).antisymm h)
 #align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_le
 
+/- warning: is_R_or_C.re_eq_self_of_le -> IsROrC.re_eq_self_of_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {a : K}, (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) a) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K 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(AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) a)) -> (Eq.{succ u1} K (IsROrC.ofReal.{u1} K _inst_1 (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K 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(Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) a)) a)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_leₓ'. -/
 theorem re_eq_self_of_le {a : K} (h : ‖a‖ ≤ re a) : (re a : K) = a := by
   rw [(is_real_tfae a).out 2 3, im_eq_zero_of_le h]
 #align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_le
 
 open IsAbsoluteValue
 
+/- warning: is_R_or_C.abs_re_div_norm_le_one -> IsROrC.abs_re_div_norm_le_one is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_oneₓ'. -/
 theorem abs_re_div_norm_le_one (z : K) : |re z / ‖z‖| ≤ 1 :=
   by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_re_le_norm _) (norm_nonneg _)
 #align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_one
 
+/- warning: is_R_or_C.abs_im_div_norm_le_one -> IsROrC.abs_im_div_norm_le_one is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (z : K), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLEReal (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) z) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) z))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) z) Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_oneₓ'. -/
 theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
   by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_im_le_norm _) (norm_nonneg _)
 #align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
 
+/- warning: is_R_or_C.re_eq_norm_of_mul_conj -> IsROrC.re_eq_norm_of_mul_conj is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) 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(IsROrC.toStarRing.{u1} K _inst_1)) x)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HMul.hMul.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conjₓ'. -/
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, of_real_re, norm_of_real, abs_of_nonneg (norm_sq_nonneg _)]
 #align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj
 
+/- warning: is_R_or_C.norm_sq_re_add_conj -> IsROrC.norm_sq_re_add_conj is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (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)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K 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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) x (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (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 {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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(RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Nat Real (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) (HAdd.hAdd.{u1, u1, u1} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) Real.instMonoidReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) x (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, 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(CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conjₓ'. -/
 theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
   rw [add_conj, norm_mul, norm_two, norm_of_real, two_mul (re x : K), map_add, of_real_re, ←
     two_mul, mul_pow, mul_pow, sq_abs]
 #align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conj
 
+/- warning: is_R_or_C.norm_sq_re_conj_add -> IsROrC.norm_sq_re_conj_add is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toHasAdd.{u1} K (Ring.toDistrib.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} 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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (x : K), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) 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(NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Nat Real (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => Real) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) Real.instMonoidReal)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddZeroClass.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) Real (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Semiring.toNonUnitalSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Field.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (NormedField.toNormedCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (DenselyNormedField.toNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) (IsROrC.toDenselyNormedField.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) x) _inst_1))))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)) x) x)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_addₓ'. -/
 theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2 := by
   rw [add_comm, norm_sq_re_add_conj]
 #align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_add
@@ -754,26 +1496,56 @@ theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2
 /-! ### Cauchy sequences -/
 
 
+/- warning: is_R_or_C.is_cau_seq_re -> IsROrC.isCauSeq_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (f : CauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1) (coeFn.{succ u1, succ u1} (CauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (fun (_x : CauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) => Nat -> K) (CauSeq.hasCoeToFun.{0, u1} Real K Real.linearOrderedField (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) f n))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (f : CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1) (Subtype.val.{succ u1} (Nat -> K) (fun (f : Nat -> K) => IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) f) f n))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_cau_seq_re IsROrC.isCauSeq_reₓ'. -/
 theorem isCauSeq_re (f : CauSeq K norm) : IsCauSeq abs fun n => re (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_re_le_norm (f j - f i)) (H _ ij)
 #align is_R_or_C.is_cau_seq_re IsROrC.isCauSeq_re
 
+/- warning: is_R_or_C.is_cau_seq_im -> IsROrC.isCauSeq_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (f : CauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1) (coeFn.{succ u1, succ u1} (CauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (fun (_x : CauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) => Nat -> K) (CauSeq.hasCoeToFun.{0, u1} Real K Real.linearOrderedField (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) f n))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] (f : CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1) (Subtype.val.{succ u1} (Nat -> K) (fun (f : Nat -> K) => IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) f) f n))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_cau_seq_im IsROrC.isCauSeq_imₓ'. -/
 theorem isCauSeq_im (f : CauSeq K norm) : IsCauSeq abs fun n => im (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_im_le_norm (f j - f i)) (H _ ij)
 #align is_R_or_C.is_cau_seq_im IsROrC.isCauSeq_im
 
+/- warning: is_R_or_C.cau_seq_re -> IsROrC.cauSeqRe is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], (CauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], (CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.cau_seq_re IsROrC.cauSeqReₓ'. -/
 /-- The real part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_re f⟩
 #align is_R_or_C.cau_seq_re IsROrC.cauSeqRe
 
+/- warning: is_R_or_C.cau_seq_im -> IsROrC.cauSeqIm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], (CauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], (CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.cau_seq_im IsROrC.cauSeqImₓ'. -/
 /-- The imaginary part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_im f⟩
 #align is_R_or_C.cau_seq_im IsROrC.cauSeqIm
 
+/- warning: is_R_or_C.is_cau_seq_norm -> IsROrC.isCauSeq_norm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {f : Nat -> K}, (IsCauSeq.{0, u1} Real Real.linearOrderedField K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) f) -> (IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (Function.comp.{1, succ u1, 1} Nat K Real (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) f))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K] {f : Nat -> K}, (IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, succ u1, 1} Nat K Real (Norm.norm.{u1} K (NormedField.toNorm.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) f))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.is_cau_seq_norm IsROrC.isCauSeq_normₓ'. -/
 theorem isCauSeq_norm {f : ℕ → K} (hf : IsCauSeq norm f) : IsCauSeq abs (norm ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
   ⟨i, fun j hj => lt_of_le_of_lt (abs_norm_sub_norm_le _ _) (hi j hj)⟩
@@ -783,6 +1555,7 @@ end IsROrC
 
 section Instances
 
+#print Real.isROrC /-
 noncomputable instance Real.isROrC : IsROrC ℝ :=
   { Real.denselyNormedField,
     Real.metricSpace with
@@ -808,6 +1581,7 @@ noncomputable instance Real.isROrC : IsROrC ℝ :=
         AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
     mul_im_i_ax := fun z => by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply] }
 #align real.is_R_or_C Real.isROrC
+-/
 
 end Instances
 
@@ -829,137 +1603,243 @@ local notation "IR" => @IsROrC.i ℝ _
 -- mathport name: exprnorm_sqR
 local notation "norm_sqR" => @IsROrC.normSq ℝ _
 
+/- warning: is_R_or_C.re_to_real -> IsROrC.re_to_real is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Eq.{1} Real (coeFn.{1, 1} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Real -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{0} Real Real.isROrC) x) x
+but is expected to have type
+  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real Real (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{0} Real Real.isROrC) x) x
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_to_real IsROrC.re_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem re_to_real {x : ℝ} : reR x = x :=
   rfl
 #align is_R_or_C.re_to_real IsROrC.re_to_real
 
+/- warning: is_R_or_C.im_to_real -> IsROrC.im_to_real is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Eq.{1} Real (coeFn.{1, 1} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Real -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{0} Real Real.isROrC) x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real Real (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Real Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonUnitalSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real (Field.toCommRing.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{0} Real Real.isROrC) x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) x) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Real) => Real) x) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_to_real IsROrC.im_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem im_to_real {x : ℝ} : imR x = 0 :=
   rfl
 #align is_R_or_C.im_to_real IsROrC.im_to_real
 
+/- warning: is_R_or_C.conj_to_real -> IsROrC.conj_to_real is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Eq.{1} Real (coeFn.{1, 1} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (fun (_x : RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) => Real -> Real) (RingHom.hasCoeToFun.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (starRingEnd.{0} Real Real.commSemiring Real.starRing) x) x
+but is expected to have type
+  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (RingHom.instRingHomClassRingHom.{0, 0} Real Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))))) (starRingEnd.{0} Real Real.instCommSemiringReal Real.instStarRingRealToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x) x
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_to_real IsROrC.conj_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conj_to_real {x : ℝ} : conj x = x :=
   rfl
 #align is_R_or_C.conj_to_real IsROrC.conj_to_real
 
+/- warning: is_R_or_C.I_to_real -> IsROrC.I_to_real is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (IsROrC.i.{0} Real Real.isROrC) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} Real (IsROrC.I.{0} Real Real.isROrC) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.I_to_real IsROrC.I_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
-theorem i_to_real : IR = 0 :=
+theorem I_to_real : IR = 0 :=
   rfl
-#align is_R_or_C.I_to_real IsROrC.i_to_real
-
+#align is_R_or_C.I_to_real IsROrC.I_to_real
+
+/- warning: is_R_or_C.norm_sq_to_real -> IsROrC.normSq_to_real is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Real -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{0} Real Real.isROrC) x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x x)
+but is expected to have type
+  forall {x : Real}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))))) (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} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{0} Real Real.isROrC) x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_realₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [IsROrC.normSq]
 #align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_real
 
+#print IsROrC.ofReal_real_eq_id /-
 @[simp]
-theorem coe_real_eq_id : @coe ℝ ℝ _ = id :=
+theorem ofReal_real_eq_id : @coe ℝ ℝ _ = id :=
   rfl
-#align is_R_or_C.coe_real_eq_id IsROrC.coe_real_eq_id
+#align is_R_or_C.coe_real_eq_id IsROrC.ofReal_real_eq_id
+-/
 
 end CleanupLemmas
 
 section LinearMaps
 
+#print IsROrC.reLm /-
 /-- The real part in a `is_R_or_C` field, as a linear map. -/
 def reLm : K →ₗ[ℝ] ℝ :=
   { re with map_smul' := smul_re }
 #align is_R_or_C.re_lm IsROrC.reLm
+-/
 
+/- warning: is_R_or_C.re_lm_coe -> IsROrC.reLm_coe is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (IsROrC.reLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) (fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid 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(AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.403 : K) => Real) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.re.{u1} K _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_lm_coe IsROrC.reLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem reLm_coe : (reLm : K → ℝ) = re :=
   rfl
 #align is_R_or_C.re_lm_coe IsROrC.reLm_coe
 
+#print IsROrC.reClm /-
 /-- The real part in a `is_R_or_C` field, as a continuous linear map. -/
 noncomputable def reClm : K →L[ℝ] ℝ :=
   LinearMap.mkContinuous reLm 1 fun x => by
     rw [one_mul]
     exact abs_re_le_norm x
 #align is_R_or_C.re_clm IsROrC.reClm
+-/
 
+#print IsROrC.reClm_coe /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem reClm_coe : ((reClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
   rfl
 #align is_R_or_C.re_clm_coe IsROrC.reClm_coe
+-/
 
+/- warning: is_R_or_C.re_clm_apply -> IsROrC.reClm_apply is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (IsROrC.reClm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K 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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.re_clm_apply IsROrC.reClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem reClm_apply : ((reClm : K →L[ℝ] ℝ) : K → ℝ) = re :=
   rfl
 #align is_R_or_C.re_clm_apply IsROrC.reClm_apply
 
+/- warning: is_R_or_C.continuous_re -> IsROrC.continuous_re is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.re.{u1} K _inst_1))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_re IsROrC.continuous_reₓ'. -/
 @[continuity]
 theorem continuous_re : Continuous (re : K → ℝ) :=
   reClm.Continuous
 #align is_R_or_C.continuous_re IsROrC.continuous_re
 
+#print IsROrC.imLm /-
 /-- The imaginary part in a `is_R_or_C` field, as a linear map. -/
 def imLm : K →ₗ[ℝ] ℝ :=
   { im with map_smul' := smul_im }
 #align is_R_or_C.im_lm IsROrC.imLm
+-/
 
+/- warning: is_R_or_C.im_lm_coe -> IsROrC.imLm_coe is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real 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(NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) (fun (_x : LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (LinearMap.hasCoeToFun.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.imLm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : K) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} Real Real K Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (IsROrC.imLm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_lm_coe IsROrC.imLm_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem imLm_coe : (imLm : K → ℝ) = im :=
   rfl
 #align is_R_or_C.im_lm_coe IsROrC.imLm_coe
 
+#print IsROrC.imClm /-
 /-- The imaginary part in a `is_R_or_C` field, as a continuous linear map. -/
 noncomputable def imClm : K →L[ℝ] ℝ :=
   LinearMap.mkContinuous imLm 1 fun x => by
     rw [one_mul]
     exact abs_im_le_norm x
 #align is_R_or_C.im_clm IsROrC.imClm
+-/
 
+#print IsROrC.imClm_coe /-
 @[simp, is_R_or_C_simps, norm_cast]
 theorem imClm_coe : ((imClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
   rfl
 #align is_R_or_C.im_clm_coe IsROrC.imClm_coe
+-/
 
+/- warning: is_R_or_C.im_clm_apply -> IsROrC.imClm_apply is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (IsROrC.imClm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) => K -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real.module) (IsROrC.imClm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => Real) a) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))) K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (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))))) (IsROrC.imClm.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.im_clm_apply IsROrC.imClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem imClm_apply : ((imClm : K →L[ℝ] ℝ) : K → ℝ) = im :=
   rfl
 #align is_R_or_C.im_clm_apply IsROrC.imClm_apply
 
+/- warning: is_R_or_C.continuous_im -> IsROrC.continuous_im is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => K -> Real) (AddMonoidHom.hasCoeToFun.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddMonoidWithOne.toAddMonoid.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (IsROrC.im.{u1} K _inst_1))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} 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.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddZeroClass.toAdd.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{u1, 0} K Real (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonUnitalSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (Field.toCommRing.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) (IsROrC.im.{u1} K _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_im IsROrC.continuous_imₓ'. -/
 @[continuity]
 theorem continuous_im : Continuous (im : K → ℝ) :=
   imClm.Continuous
 #align is_R_or_C.continuous_im IsROrC.continuous_im
 
+#print IsROrC.conjAe /-
 /-- Conjugate as an `ℝ`-algebra equivalence -/
 def conjAe : K ≃ₐ[ℝ] K :=
   { conj with
     invFun := conj
     left_inv := conj_conj
     right_inv := conj_conj
-    commutes' := conj_of_real }
+    commutes' := conj_ofReal }
 #align is_R_or_C.conj_ae IsROrC.conjAe
+-/
 
+/- warning: is_R_or_C.conj_ae_coe -> IsROrC.conjAe_coe is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : AlgEquiv.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K 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(NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) => K -> K) (AlgEquiv.hasCoeToFun.{0, u1, u1} Real K K Real.commSemiring (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (Ring.toSemiring.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K 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+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) 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(IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (SMulZeroClass.toSMul.{0, u1} Real K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{0, u1} Real K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (DistribMulAction.toDistribSMul.{0, u1} Real K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (Module.toDistribMulAction.{0, u1} Real K (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (Algebra.toModule.{0, u1} Real K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{0, u1, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (AlgEquivClass.toAlgHomClass.{u1, 0, u1, u1} (AlgEquiv.{0, u1, u1} Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) Real K K Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) (NormedAlgebra.toAlgebra.{0, u1} Real K Real.normedField (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)) 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(NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_ae_coe IsROrC.conjAe_coeₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjAe_coe : (conjAe : K → K) = conj :=
   rfl
 #align is_R_or_C.conj_ae_coe IsROrC.conjAe_coe
 
+#print IsROrC.conjLie /-
 /-- Conjugate as a linear isometry -/
 noncomputable def conjLie : K ≃ₗᵢ[ℝ] K :=
   ⟨conjAe.toLinearEquiv, fun _ => norm_conj⟩
 #align is_R_or_C.conj_lie IsROrC.conjLie
+-/
 
+/- warning: is_R_or_C.conj_lie_apply -> IsROrC.conjLie_apply is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K 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(LinearIsometryEquiv.hasCoeToFun.{0, 0, u1, u1} Real Real K K 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.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K 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(NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.conjLie.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, u1} (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, u1, u1, u1} Real Real K K (LinearIsometryEquiv.{0, 0, u1, u1} 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) K K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K 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+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_lie_apply IsROrC.conjLie_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjLie_apply : (conjLie : K → K) = conj :=
   rfl
 #align is_R_or_C.conj_lie_apply IsROrC.conjLie_apply
 
+#print IsROrC.conjCle /-
 /-- Conjugate as a continuous linear equivalence -/
 noncomputable def conjCle : K ≃L[ℝ] K :=
   @conjLie K _
 #align is_R_or_C.conj_cle IsROrC.conjCle
+-/
 
+#print IsROrC.conjCle_coe /-
 @[simp, is_R_or_C_simps]
 theorem conjCle_coe : (@conjCle K _).toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
 #align is_R_or_C.conj_cle_coe IsROrC.conjCle_coe
+-/
 
+/- warning: is_R_or_C.conj_cle_apply -> IsROrC.conjCle_apply is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => K -> K) (IsROrC.conjCle.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (fun (_x : ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => K -> K) (ContinuousLinearEquiv.hasCoeToFun.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.conjCle.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : K), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) a) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K (fun (_x : K) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : K) => K) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, 0, 0, u1, u1} (ContinuousLinearEquiv.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{0, 0, u1, u1} 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) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (IsROrC.conjCle.{u1} K _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => K) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.conj_cle_apply IsROrC.conjCle_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem conjCle_apply : (conjCle : K → K) = conj :=
   rfl
@@ -968,53 +1848,89 @@ theorem conjCle_apply : (conjCle : K → K) = conj :=
 instance (priority := 100) : ContinuousStar K :=
   ⟨conjLie.Continuous⟩
 
+/- warning: is_R_or_C.continuous_conj -> IsROrC.continuous_conj is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, u1} K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (fun (_x : RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) => K -> K) (RingHom.hasCoeToFun.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, u1} K K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K 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(NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (RingHom.instRingHomClassRingHom.{u1, u1} K K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))))) (starRingEnd.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))) (IsROrC.toStarRing.{u1} K _inst_1)))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_conj IsROrC.continuous_conjₓ'. -/
 @[continuity]
 theorem continuous_conj : Continuous (conj : K → K) :=
   continuous_star
 #align is_R_or_C.continuous_conj IsROrC.continuous_conj
 
+#print IsROrC.ofRealAm /-
 /-- The `ℝ → K` coercion, as a linear map -/
 noncomputable def ofRealAm : ℝ →ₐ[ℝ] K :=
   Algebra.ofId ℝ K
 #align is_R_or_C.of_real_am IsROrC.ofRealAm
+-/
 
+#print IsROrC.ofRealAm_coe /-
 @[simp, is_R_or_C_simps]
 theorem ofRealAm_coe : (ofRealAm : ℝ → K) = coe :=
   rfl
 #align is_R_or_C.of_real_am_coe IsROrC.ofRealAm_coe
+-/
 
+#print IsROrC.ofRealLi /-
 /-- The ℝ → K coercion, as a linear isometry -/
 noncomputable def ofRealLi : ℝ →ₗᵢ[ℝ] K
     where
   toLinearMap := ofRealAm.toLinearMap
-  norm_map' := norm_of_real
+  norm_map' := norm_ofReal
 #align is_R_or_C.of_real_li IsROrC.ofRealLi
+-/
 
+/- warning: is_R_or_C.of_real_li_apply -> IsROrC.ofRealLi_apply is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => Real -> K) (IsROrC.ofRealLi.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (fun (_x : LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => Real -> K) (LinearIsometry.hasCoeToFun.{0, 0, 0, u1} Real Real Real K Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.ofRealLi.{u1} K _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : Real), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => K) a) (FunLike.coe.{succ u1, 1, succ u1} (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => K) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real K (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, 0, u1} (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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 (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))))) (AddCommGroup.toAddCommMonoid.{0} Real (SeminormedAddCommGroup.toAddCommGroup.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (AddCommGroup.toAddCommMonoid.{u1} K (SeminormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, u1, u1} Real Real Real K (LinearIsometry.{0, 0, 0, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real K (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{0, 0, 0, u1} Real Real Real K Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))))))) (IsROrC.ofRealLi.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_li_apply IsROrC.ofRealLi_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem ofRealLi_apply : (ofRealLi : ℝ → K) = coe :=
   rfl
 #align is_R_or_C.of_real_li_apply IsROrC.ofRealLi_apply
 
+#print IsROrC.ofRealClm /-
 /-- The `ℝ → K` coercion, as a continuous linear map -/
 noncomputable def ofRealClm : ℝ →L[ℝ] K :=
   ofRealLi.toContinuousLinearMap
 #align is_R_or_C.of_real_clm IsROrC.ofRealClm
+-/
 
+#print IsROrC.ofRealClm_coe /-
 @[simp, is_R_or_C_simps]
 theorem ofRealClm_coe : (@ofRealClm K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinearMap :=
   rfl
 #align is_R_or_C.of_real_clm_coe IsROrC.ofRealClm_coe
+-/
 
+/- warning: is_R_or_C.of_real_clm_apply -> IsROrC.ofRealClm_apply is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} ((fun (_x : ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => Real -> K) (IsROrC.ofRealClm.{u1} K _inst_1)) (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K 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(IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) => Real -> K) (ContinuousLinearMap.toFun.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) Real.module (NormedSpace.toModule.{0, u1} Real K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) (IsROrC.ofRealClm.{u1} K _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real K (HasLiftT.mk.{1, succ u1} Real K (CoeTCₓ.coe.{1, succ u1} Real K (IsROrC.algebraMapCoe.{u1} K _inst_1))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Eq.{succ u1} (forall (a : Real), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => K) a) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) Real K (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, 0, u1} (ContinuousLinearMap.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))) 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1))) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, 0, u1} 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 K (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (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 K Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} K (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))) (IsROrC.toNormedAlgebra.{u1} K _inst_1)))))) (IsROrC.ofRealClm.{u1} K _inst_1)) (IsROrC.ofReal.{u1} K _inst_1)
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.of_real_clm_apply IsROrC.ofRealClm_applyₓ'. -/
 @[simp, is_R_or_C_simps]
 theorem ofRealClm_apply : (ofRealClm : ℝ → K) = coe :=
   rfl
 #align is_R_or_C.of_real_clm_apply IsROrC.ofRealClm_apply
 
+#print IsROrC.continuous_ofReal /-
 @[continuity]
-theorem continuous_of_real : Continuous (coe : ℝ → K) :=
+theorem continuous_ofReal : Continuous (coe : ℝ → K) :=
   ofRealLi.Continuous
-#align is_R_or_C.continuous_of_real IsROrC.continuous_of_real
+#align is_R_or_C.continuous_of_real IsROrC.continuous_ofReal
+-/
 
+/- warning: is_R_or_C.continuous_norm_sq -> IsROrC.continuous_normSq is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => K -> Real) (MonoidWithZeroHom.hasCoeToFun.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (IsROrC.normSq.{u1} K _inst_1))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : IsROrC.{u1} K], Continuous.{u1, 0} K Real (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Real) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulOneClass.toMul.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1))))))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, 0} (MonoidWithZeroHom.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, 0} K Real (NonAssocSemiring.toMulZeroOneClass.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K (DenselyNormedField.toNormedField.{u1} K (IsROrC.toDenselyNormedField.{u1} K _inst_1)))))))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) (IsROrC.normSq.{u1} K _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_R_or_C.continuous_norm_sq IsROrC.continuous_normSqₓ'. -/
 @[continuity]
 theorem continuous_normSq : Continuous (normSq : K → ℝ) :=
   (continuous_re.mul continuous_re).add (continuous_im.mul continuous_im)

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: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit 25580801f04aed44a0daf912d3760d0eaaf6d1bb
+! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -146,12 +146,13 @@ theorem ext {z w : K} (hre : re z = re w) (him : im z = im w) : z = w :=
 #align is_R_or_C.ext IsROrC.ext
 
 @[norm_cast]
-theorem of_real_zero : ((0 : ℝ) : K) = 0 := by rw [of_real_alg, zero_smul]
+theorem of_real_zero : ((0 : ℝ) : K) = 0 :=
+  algebraMap.coe_zero
 #align is_R_or_C.of_real_zero IsROrC.of_real_zero
 
-@[simp, is_R_or_C_simps]
+@[is_R_or_C_simps]
 theorem zero_re' : re (0 : K) = (0 : ℝ) :=
-  re.map_zero
+  map_zero re
 #align is_R_or_C.zero_re' IsROrC.zero_re'
 
 @[norm_cast]
@@ -263,11 +264,9 @@ theorem of_real_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α
 #align is_R_or_C.of_real_finsupp_prod IsROrC.of_real_finsupp_prod
 
 @[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_smul (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
-  by
-  simp_rw [← smul_eq_mul, of_real_alg r]
-  simp only [Algebra.id.smul_eq_mul, one_mul, Algebra.smul_mul_assoc]
-#align is_R_or_C.of_real_smul IsROrC.of_real_smul
+theorem real_smul_of_real (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
+  real_smul_eq_coe_mul _ _
+#align is_R_or_C.real_smul_of_real IsROrC.real_smul_of_real
 
 @[is_R_or_C_simps]
 theorem of_real_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
@@ -280,23 +279,28 @@ theorem of_real_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
 #align is_R_or_C.of_real_mul_im IsROrC.of_real_mul_im
 
 @[is_R_or_C_simps]
-theorem smul_re : ∀ (r : ℝ) (z : K), re (r • z) = r * re z := fun r z =>
-  by
-  rw [Algebra.smul_def]
-  apply of_real_mul_re
+theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
+  rw [real_smul_eq_coe_mul, of_real_mul_re]
 #align is_R_or_C.smul_re IsROrC.smul_re
 
 @[is_R_or_C_simps]
-theorem smul_im : ∀ (r : ℝ) (z : K), im (r • z) = r * im z := fun r z =>
-  by
-  rw [Algebra.smul_def]
-  apply of_real_mul_im
+theorem smul_im (r : ℝ) (z : K) : im (r • z) = r * im z := by
+  rw [real_smul_eq_coe_mul, of_real_mul_im]
 #align is_R_or_C.smul_im IsROrC.smul_im
 
-@[simp, is_R_or_C_simps]
-theorem norm_real (r : ℝ) : ‖(r : K)‖ = ‖r‖ := by
-  rw [IsROrC.of_real_alg, norm_smul, norm_one, mul_one]
-#align is_R_or_C.norm_real IsROrC.norm_real
+@[simp, norm_cast, is_R_or_C_simps]
+theorem norm_of_real (r : ℝ) : ‖(r : K)‖ = |r| :=
+  norm_algebraMap' K r
+#align is_R_or_C.norm_of_real IsROrC.norm_of_real
+
+/-! ### Characteristic zero -/
+
+
+-- see Note [lower instance priority]
+/-- ℝ and ℂ are both of characteristic zero.  -/
+instance (priority := 100) charZero_R_or_C : CharZero K :=
+  (RingHom.charZero_iff (algebraMap ℝ K).Injective).1 inferInstance
+#align is_R_or_C.char_zero_R_or_C IsROrC.charZero_R_or_C
 
 /-! ### The imaginary unit, `I` -/
 
@@ -362,41 +366,65 @@ theorem conj_neg_i : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
 #align is_R_or_C.conj_neg_I IsROrC.conj_neg_i
 
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
-  by
-  rw [ext_iff]
-  simp only [add_zero, I_re, of_real_im, I_im, zero_sub, MulZeroClass.zero_mul, conj_im, of_real_re,
-    eq_self_iff_true, sub_zero, conj_re, mul_im, neg_inj, and_self_iff, mul_re,
-    MulZeroClass.mul_zero, map_sub]
+  (congr_arg conj (re_add_im z).symm).trans <| by
+    rw [map_add, map_mul, conj_I, conj_of_real, conj_of_real, mul_neg, sub_eq_add_neg]
 #align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_im
 
-@[is_R_or_C_simps]
-theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z :=
+theorem sub_conj (z : K) : z - conj z = 2 * im z * i :=
   by
-  simp_rw [conj_eq_re_sub_im]
-  simp only [smul_re, smul_im, of_real_mul]
-  rw [smul_sub]
-  simp_rw [of_real_alg]
-  simp only [one_mul, Algebra.smul_mul_assoc]
+  nth_rw 1 [← re_add_im z]
+  rw [conj_eq_re_sub_im, add_sub_sub_cancel, ← two_mul, mul_assoc]
+#align is_R_or_C.sub_conj IsROrC.sub_conj
+
+@[is_R_or_C_simps]
+theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
+  rw [conj_eq_re_sub_im, conj_eq_re_sub_im, smul_re, smul_im, of_real_mul, of_real_mul,
+    real_smul_eq_coe_mul, mul_sub, mul_assoc]
 #align is_R_or_C.conj_smul IsROrC.conj_smul
 
-theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
+theorem add_conj (z : K) : z + conj z = 2 * re z :=
+  calc
+    z + conj z = re z + im z * i + (re z - im z * i) := by rw [re_add_im, conj_eq_re_sub_im]
+    _ = 2 * re z := by rw [add_add_sub_cancel, two_mul]
+    
+#align is_R_or_C.add_conj IsROrC.add_conj
+
+theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
+  rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
+#align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
+
+theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 := by
+  rw [← neg_inj, ← of_real_neg, ← I_mul_re, re_eq_add_conj, map_mul, conj_I, ← neg_div, ← mul_neg,
+    neg_sub, mul_sub, neg_mul, sub_eq_add_neg]
+#align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_sub
+
+/-- There are several equivalent ways to say that a number `z` is in fact a real number. -/
+theorem is_real_tFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] :=
   by
-  constructor
+  tfae_have 1 → 4
+  · intro h
+    rw [← @of_real_inj K, im_eq_conj_sub, h, sub_self, MulZeroClass.mul_zero, zero_div,
+      of_real_zero]
+  tfae_have 4 → 3
   · intro h
-    suffices im z = 0 by
-      use re z
-      rw [← add_zero (coe _)]
-      convert(re_add_im z).symm
-      simp [this]
-    contrapose! h
-    rw [← re_add_im z]
-    simp only [conj_of_real, RingHom.map_add, RingHom.map_mul, conj_I_ax]
-    rw [add_left_cancel_iff, ext_iff]
-    simpa [neg_eq_iff_add_eq_zero, add_self_eq_zero]
-  · rintro ⟨r, rfl⟩
-    apply conj_of_real
+    conv_rhs => rw [← re_add_im z, h, of_real_zero, MulZeroClass.zero_mul, add_zero]
+  tfae_have 3 → 2; exact fun h => ⟨_, h⟩
+  tfae_have 2 → 1; exact fun ⟨r, hr⟩ => hr ▸ conj_of_real _
+  tfae_finish
+#align is_R_or_C.is_real_tfae IsROrC.is_real_tFAE
+
+theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
+  ((is_real_tFAE z).out 0 1).trans <| by simp only [eq_comm]
 #align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_real
 
+theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
+  (is_real_tFAE z).out 0 2
+#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
+
+theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
+  (is_real_tFAE z).out 0 3
+#align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_im
+
 @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
   rfl
@@ -412,10 +440,6 @@ abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
 
 variable {K}
 
-theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
-  conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
-#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
-
 /-- The norm squared function. -/
 def normSq : K →*₀ ℝ where
   toFun z := re z * re z + im z * im z
@@ -426,14 +450,16 @@ def normSq : K →*₀ ℝ where
     ring
 #align is_R_or_C.norm_sq IsROrC.normSq
 
+theorem normSq_apply (z : K) : normSq z = re z * re z + im z * im z :=
+  rfl
+#align is_R_or_C.norm_sq_apply IsROrC.normSq_apply
+
 theorem norm_sq_eq_def {z : K} : ‖z‖ ^ 2 = re z * re z + im z * im z :=
   norm_sq_eq_def_ax z
 #align is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_def
 
 theorem normSq_eq_def' (z : K) : normSq z = ‖z‖ ^ 2 :=
-  by
-  rw [norm_sq_eq_def]
-  rfl
+  norm_sq_eq_def.symm
 #align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'
 
 @[is_R_or_C_simps]
@@ -468,7 +494,7 @@ theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [norm_sq_eq_
 
 @[simp, is_R_or_C_simps]
 theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
-  simp only [norm_sq, neg_mul, MonoidWithZeroHom.coe_mk, mul_neg, neg_neg, is_R_or_C_simps]
+  simp only [norm_sq_apply, neg_mul, mul_neg, neg_neg, is_R_or_C_simps]
 #align is_R_or_C.norm_sq_conj IsROrC.normSq_conj
 
 @[simp, is_R_or_C_simps]
@@ -478,7 +504,7 @@ theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
 
 theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) :=
   by
-  simp only [norm_sq, map_add, MonoidWithZeroHom.coe_mk, mul_neg, sub_neg_eq_add, is_R_or_C_simps]
+  simp only [norm_sq_apply, map_add, mul_neg, sub_neg_eq_add, is_R_or_C_simps]
   ring
 #align is_R_or_C.norm_sq_add IsROrC.normSq_add
 
@@ -491,26 +517,15 @@ theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
 #align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
 
 theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
-  simp only [map_add, add_zero, ext_iff, MonoidWithZeroHom.coe_mk, add_left_inj,
-    mul_eq_mul_left_iff, MulZeroClass.zero_mul, add_comm, true_or_iff, eq_self_iff_true, mul_neg,
-    add_right_neg, zero_add, norm_sq, mul_comm, and_self_iff, neg_neg, MulZeroClass.mul_zero,
-    sub_eq_neg_add, neg_zero, is_R_or_C_simps]
+  simp only [map_add, add_zero, ext_iff, add_left_inj, mul_eq_mul_left_iff, MulZeroClass.zero_mul,
+    add_comm, true_or_iff, eq_self_iff_true, mul_neg, add_right_neg, zero_add, norm_sq_apply,
+    mul_comm, and_self_iff, neg_neg, MulZeroClass.mul_zero, sub_eq_neg_add, neg_zero,
+    is_R_or_C_simps]
 #align is_R_or_C.mul_conj IsROrC.mul_conj
 
 theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
 #align is_R_or_C.conj_mul IsROrC.conj_mul
 
-theorem add_conj (z : K) : z + conj z = 2 * re z := by
-  simp only [ext_iff, two_mul, map_add, add_zero, of_real_im, conj_im, of_real_re, eq_self_iff_true,
-    add_right_neg, conj_re, and_self_iff]
-#align is_R_or_C.add_conj IsROrC.add_conj
-
-theorem sub_conj (z : K) : z - conj z = 2 * im z * i := by
-  simp only [ext_iff, two_mul, sub_eq_add_neg, add_mul, map_add, add_zero, add_left_inj,
-    MulZeroClass.zero_mul, map_add_neg, eq_self_iff_true, add_right_neg, and_self_iff, neg_neg,
-    MulZeroClass.mul_zero, neg_zero, is_R_or_C_simps]
-#align is_R_or_C.sub_conj IsROrC.sub_conj
-
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [norm_sq_add, sub_eq_add_neg, RingEquiv.map_neg, mul_neg, norm_sq_neg, map_neg]
 #align is_R_or_C.norm_sq_sub IsROrC.normSq_sub
@@ -580,16 +595,15 @@ theorem i_mul_i_of_nonzero : (i : K) ≠ 0 → (i : K) * i = -1 :=
 #align is_R_or_C.I_mul_I_of_nonzero IsROrC.i_mul_i_of_nonzero
 
 @[simp, is_R_or_C_simps]
-theorem div_i (z : K) : z / i = -(z * i) :=
-  by
+theorem inv_i : (i : K)⁻¹ = -i := by
   by_cases h : (I : K) = 0
   · simp [h]
-  · field_simp [mul_assoc, I_mul_I_of_nonzero h]
-#align is_R_or_C.div_I IsROrC.div_i
+  · field_simp [I_mul_I_of_nonzero h]
+#align is_R_or_C.inv_I IsROrC.inv_i
 
 @[simp, is_R_or_C_simps]
-theorem inv_i : (i : K)⁻¹ = -i := by field_simp
-#align is_R_or_C.inv_I IsROrC.inv_i
+theorem div_i (z : K) : z / i = -(z * i) := by rw [div_eq_mul_inv, inv_I, mul_neg]
+#align is_R_or_C.div_I IsROrC.div_i
 
 @[simp, is_R_or_C_simps]
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
@@ -601,7 +615,7 @@ theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ (@normSq K _) z w
 #align is_R_or_C.norm_sq_div IsROrC.normSq_div
 
-@[is_R_or_C_simps]
+@[simp, is_R_or_C_simps]
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_norm_sq_eq_norm, norm_sq_conj]
 #align is_R_or_C.norm_conj IsROrC.norm_conj
 
@@ -650,279 +664,120 @@ theorem rat_cast_re (q : ℚ) : re (q : K) = q := by rw [← of_real_rat_cast, o
 theorem rat_cast_im (q : ℚ) : im (q : K) = 0 := by rw [← of_real_rat_cast, of_real_im]
 #align is_R_or_C.rat_cast_im IsROrC.rat_cast_im
 
-/-! ### Characteristic zero -/
-
-
--- see Note [lower instance priority]
-/-- ℝ and ℂ are both of characteristic zero.  -/
-instance (priority := 100) charZero_R_or_C : CharZero K :=
-  charZero_of_inj_zero fun n h => by
-    rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h
-#align is_R_or_C.char_zero_R_or_C IsROrC.charZero_R_or_C
-
-theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
-  rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
-#align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
-
-theorem im_eq_conj_sub (z : K) : ↑(im z) = i * (conj z - z) / 2 :=
-  by
-  rw [← neg_inj, ← of_real_neg, ← I_mul_re, re_eq_add_conj]
-  simp only [mul_add, sub_eq_add_neg, neg_div', neg_mul, conj_I, mul_neg, neg_add_rev, neg_neg,
-    RingHom.map_mul]
-#align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_sub
-
-/-! ### Absolute value -/
-
-
-/-- The complex absolute value function, defined as the square root of the norm squared. -/
-@[pp_nodot]
-noncomputable def abs (z : K) : ℝ :=
-  (normSq z).sqrt
-#align is_R_or_C.abs IsROrC.abs
-
--- mathport name: exprabs'
-local notation "abs'" => Abs.abs
-
--- mathport name: exprabsK
-local notation "absK" => @abs K _
-
-@[simp, norm_cast]
-theorem abs_of_real (r : ℝ) : absK r = abs' r := by
-  simp only [abs, norm_sq, Real.sqrt_mul_self_eq_abs, add_zero, of_real_im,
-    MonoidWithZeroHom.coe_mk, of_real_re, MulZeroClass.mul_zero]
-#align is_R_or_C.abs_of_real IsROrC.abs_of_real
+/-! ### Norm -/
 
-theorem norm_eq_abs (z : K) : ‖z‖ = absK z := by
-  simp only [abs, norm_sq_eq_def', norm_nonneg, Real.sqrt_sq]
-#align is_R_or_C.norm_eq_abs IsROrC.norm_eq_abs
 
-@[is_R_or_C_simps, norm_cast]
-theorem norm_of_real (z : ℝ) : ‖(z : K)‖ = ‖z‖ := by
-  rw [IsROrC.norm_eq_abs, IsROrC.abs_of_real, Real.norm_eq_abs]
-#align is_R_or_C.norm_of_real IsROrC.norm_of_real
-
-theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : absK r = r :=
-  (abs_of_real _).trans (abs_of_nonneg h)
-#align is_R_or_C.abs_of_nonneg IsROrC.abs_of_nonneg
-
-theorem norm_of_nonneg {r : ℝ} (r_nn : 0 ≤ r) : ‖(r : K)‖ = r :=
-  by
-  rw [norm_of_real]
-  exact abs_eq_self.mpr r_nn
+theorem norm_of_nonneg {r : ℝ} (h : 0 ≤ r) : ‖(r : K)‖ = r :=
+  (norm_of_real _).trans (abs_of_nonneg h)
 #align is_R_or_C.norm_of_nonneg IsROrC.norm_of_nonneg
 
-theorem abs_of_nat (n : ℕ) : absK n = n :=
+@[simp, is_R_or_C_simps, norm_cast]
+theorem norm_nat_cast (n : ℕ) : ‖(n : K)‖ = n :=
   by
   rw [← of_real_nat_cast]
-  exact abs_of_nonneg (Nat.cast_nonneg n)
-#align is_R_or_C.abs_of_nat IsROrC.abs_of_nat
-
-theorem mul_self_abs (z : K) : abs z * abs z = normSq z :=
-  Real.mul_self_sqrt (normSq_nonneg _)
-#align is_R_or_C.mul_self_abs IsROrC.mul_self_abs
-
-@[simp, is_R_or_C_simps]
-theorem abs_zero : absK 0 = 0 := by simp only [abs, Real.sqrt_zero, map_zero]
-#align is_R_or_C.abs_zero IsROrC.abs_zero
+  exact norm_of_nonneg (Nat.cast_nonneg n)
+#align is_R_or_C.norm_nat_cast IsROrC.norm_nat_cast
 
-@[simp, is_R_or_C_simps]
-theorem abs_one : absK 1 = 1 := by simp only [abs, map_one, Real.sqrt_one]
-#align is_R_or_C.abs_one IsROrC.abs_one
-
-@[simp, is_R_or_C_simps]
-theorem abs_two : absK 2 = 2 :=
-  calc
-    absK 2 = absK (2 : ℝ) := by rw [of_real_bit0, of_real_one]
-    _ = (2 : ℝ) := abs_of_nonneg (by norm_num)
-    
-#align is_R_or_C.abs_two IsROrC.abs_two
-
-theorem abs_nonneg (z : K) : 0 ≤ absK z :=
-  Real.sqrt_nonneg _
-#align is_R_or_C.abs_nonneg IsROrC.abs_nonneg
-
-@[simp, is_R_or_C_simps]
-theorem abs_eq_zero {z : K} : absK z = 0 ↔ z = 0 :=
-  (Real.sqrt_eq_zero <| normSq_nonneg _).trans normSq_eq_zero
-#align is_R_or_C.abs_eq_zero IsROrC.abs_eq_zero
+theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [norm_sq_eq_def', sq]
+#align is_R_or_C.mul_self_norm IsROrC.mul_self_norm
 
-theorem abs_ne_zero {z : K} : abs z ≠ 0 ↔ z ≠ 0 :=
-  not_congr abs_eq_zero
-#align is_R_or_C.abs_ne_zero IsROrC.abs_ne_zero
+attribute [is_R_or_C_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
 
 @[simp, is_R_or_C_simps]
-theorem abs_conj (z : K) : abs (conj z) = abs z := by simp only [abs, norm_sq_conj]
-#align is_R_or_C.abs_conj IsROrC.abs_conj
+theorem norm_two : ‖(2 : K)‖ = 2 := by rw [← Nat.cast_two, norm_nat_cast, Nat.cast_two]
+#align is_R_or_C.norm_two IsROrC.norm_two
 
-@[simp, is_R_or_C_simps]
-theorem abs_mul (z w : K) : abs (z * w) = abs z * abs w := by
-  rw [abs, norm_sq_mul, Real.sqrt_mul (norm_sq_nonneg _)] <;> rfl
-#align is_R_or_C.abs_mul IsROrC.abs_mul
-
-theorem abs_re_le_abs (z : K) : abs' (re z) ≤ abs z := by
-  rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (re z)) (abs_nonneg _), abs_mul_abs_self,
-      mul_self_abs] <;>
+theorem abs_re_le_norm (z : K) : |re z| ≤ ‖z‖ := by
+  rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (re z)) (norm_nonneg _), abs_mul_abs_self,
+      mul_self_norm] <;>
     apply re_sq_le_norm_sq
-#align is_R_or_C.abs_re_le_abs IsROrC.abs_re_le_abs
+#align is_R_or_C.abs_re_le_norm IsROrC.abs_re_le_norm
 
-theorem abs_im_le_abs (z : K) : abs' (im z) ≤ abs z := by
-  rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (im z)) (abs_nonneg _), abs_mul_abs_self,
-      mul_self_abs] <;>
+theorem abs_im_le_norm (z : K) : |im z| ≤ ‖z‖ := by
+  rw [mul_self_le_mul_self_iff (_root_.abs_nonneg (im z)) (norm_nonneg _), abs_mul_abs_self,
+      mul_self_norm] <;>
     apply im_sq_le_norm_sq
-#align is_R_or_C.abs_im_le_abs IsROrC.abs_im_le_abs
+#align is_R_or_C.abs_im_le_norm IsROrC.abs_im_le_norm
 
 theorem norm_re_le_norm (z : K) : ‖re z‖ ≤ ‖z‖ :=
-  by
-  rw [IsROrC.norm_eq_abs, Real.norm_eq_abs]
-  exact IsROrC.abs_re_le_abs _
+  abs_re_le_norm z
 #align is_R_or_C.norm_re_le_norm IsROrC.norm_re_le_norm
 
 theorem norm_im_le_norm (z : K) : ‖im z‖ ≤ ‖z‖ :=
-  by
-  rw [IsROrC.norm_eq_abs, Real.norm_eq_abs]
-  exact IsROrC.abs_im_le_abs _
+  abs_im_le_norm z
 #align is_R_or_C.norm_im_le_norm IsROrC.norm_im_le_norm
 
-theorem re_le_abs (z : K) : re z ≤ abs z :=
-  (abs_le.1 (abs_re_le_abs _)).2
-#align is_R_or_C.re_le_abs IsROrC.re_le_abs
+theorem re_le_norm (z : K) : re z ≤ ‖z‖ :=
+  (abs_le.1 (abs_re_le_norm z)).2
+#align is_R_or_C.re_le_norm IsROrC.re_le_norm
 
-theorem im_le_abs (z : K) : im z ≤ abs z :=
-  (abs_le.1 (abs_im_le_abs _)).2
-#align is_R_or_C.im_le_abs IsROrC.im_le_abs
+theorem im_le_norm (z : K) : im z ≤ ‖z‖ :=
+  (abs_le.1 (abs_im_le_norm _)).2
+#align is_R_or_C.im_le_norm IsROrC.im_le_norm
 
-theorem im_eq_zero_of_le {a : K} (h : abs a ≤ re a) : im a = 0 :=
-  by
-  rw [← zero_eq_mul_self]
-  have : re a * re a = re a * re a + im a * im a := by
-    convert IsROrC.mul_self_abs a <;> linarith [re_le_abs a]
-  linarith
+theorem im_eq_zero_of_le {a : K} (h : ‖a‖ ≤ re a) : im a = 0 := by
+  simpa only [mul_self_norm a, norm_sq_apply, self_eq_add_right, mul_self_eq_zero] using
+    congr_arg (fun z => z * z) ((re_le_norm a).antisymm h)
 #align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_le
 
-theorem re_eq_self_of_le {a : K} (h : abs a ≤ re a) : (re a : K) = a :=
-  by
-  rw [← re_add_im a]
-  simp only [im_eq_zero_of_le h, add_zero, MulZeroClass.zero_mul, algebraMap.coe_zero,
-    is_R_or_C_simps]
+theorem re_eq_self_of_le {a : K} (h : ‖a‖ ≤ re a) : (re a : K) = a := by
+  rw [(is_real_tfae a).out 2 3, im_eq_zero_of_le h]
 #align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_le
 
-theorem abs_add (z w : K) : abs (z + w) ≤ abs z + abs w :=
-  (mul_self_le_mul_self_iff (abs_nonneg _) (add_nonneg (abs_nonneg _) (abs_nonneg _))).2 <|
-    by
-    rw [mul_self_abs, add_mul_self_eq, mul_self_abs, mul_self_abs, add_right_comm, norm_sq_add,
-      add_le_add_iff_left, mul_assoc, mul_le_mul_left (zero_lt_two' ℝ)]
-    simpa [-mul_re, is_R_or_C_simps] using re_le_abs (z * conj w)
-#align is_R_or_C.abs_add IsROrC.abs_add
-
-instance : IsAbsoluteValue absK where
-  abv_nonneg := abs_nonneg
-  abv_eq_zero _ := abs_eq_zero
-  abv_add := abs_add
-  abv_mul := abs_mul
-
 open IsAbsoluteValue
 
-@[simp, is_R_or_C_simps]
-theorem abs_abs (z : K) : abs' (abs z) = abs z :=
-  abs_of_nonneg (abs_nonneg _)
-#align is_R_or_C.abs_abs IsROrC.abs_abs
-
-@[simp, is_R_or_C_simps]
-theorem abs_pos {z : K} : 0 < abs z ↔ z ≠ 0 :=
-  abv_pos abs
-#align is_R_or_C.abs_pos IsROrC.abs_pos
-
-@[simp, is_R_or_C_simps]
-theorem abs_neg : ∀ z : K, abs (-z) = abs z :=
-  abv_neg abs
-#align is_R_or_C.abs_neg IsROrC.abs_neg
-
-theorem abs_sub : ∀ z w : K, abs (z - w) = abs (w - z) :=
-  abv_sub abs
-#align is_R_or_C.abs_sub IsROrC.abs_sub
-
-theorem abs_sub_le : ∀ a b c : K, abs (a - c) ≤ abs (a - b) + abs (b - c) :=
-  abv_sub_le abs
-#align is_R_or_C.abs_sub_le IsROrC.abs_sub_le
-
-@[simp, is_R_or_C_simps]
-theorem abs_inv : ∀ z : K, abs z⁻¹ = (abs z)⁻¹ :=
-  abv_inv abs
-#align is_R_or_C.abs_inv IsROrC.abs_inv
-
-@[simp, is_R_or_C_simps]
-theorem abs_div : ∀ z w : K, abs (z / w) = abs z / abs w :=
-  abv_div abs
-#align is_R_or_C.abs_div IsROrC.abs_div
-
-theorem abs_abs_sub_le_abs_sub : ∀ z w : K, abs' (abs z - abs w) ≤ abs (z - w) :=
-  abs_abv_sub_le_abv_sub abs
-#align is_R_or_C.abs_abs_sub_le_abs_sub IsROrC.abs_abs_sub_le_abs_sub
-
-theorem abs_re_div_abs_le_one (z : K) : abs' (re z / abs z) ≤ 1 :=
+theorem abs_re_div_norm_le_one (z : K) : |re z / ‖z‖| ≤ 1 :=
   by
-  by_cases hz : z = 0
-  · simp [hz, zero_le_one]
-  · simp_rw [_root_.abs_div, abs_abs, div_le_iff (abs_pos.2 hz), one_mul, abs_re_le_abs]
-#align is_R_or_C.abs_re_div_abs_le_one IsROrC.abs_re_div_abs_le_one
+  rw [abs_div, abs_norm]
+  exact div_le_one_of_le (abs_re_le_norm _) (norm_nonneg _)
+#align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_one
 
-theorem abs_im_div_abs_le_one (z : K) : abs' (im z / abs z) ≤ 1 :=
+theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 :=
   by
-  by_cases hz : z = 0
-  · simp [hz, zero_le_one]
-  · simp_rw [_root_.abs_div, abs_abs, div_le_iff (abs_pos.2 hz), one_mul, abs_im_le_abs]
-#align is_R_or_C.abs_im_div_abs_le_one IsROrC.abs_im_div_abs_le_one
-
-@[simp, is_R_or_C_simps, norm_cast]
-theorem abs_cast_nat (n : ℕ) : abs (n : K) = n := by
-  rw [← of_real_nat_cast, abs_of_nonneg (Nat.cast_nonneg n)]
-#align is_R_or_C.abs_cast_nat IsROrC.abs_cast_nat
+  rw [abs_div, abs_norm]
+  exact div_le_one_of_le (abs_im_le_norm _) (norm_nonneg _)
+#align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
 
-theorem normSq_eq_abs (x : K) : normSq x = abs x ^ 2 := by
-  rw [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
-#align is_R_or_C.norm_sq_eq_abs IsROrC.normSq_eq_abs
+theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
+  rw [mul_conj, of_real_re, norm_of_real, abs_of_nonneg (norm_sq_nonneg _)]
+#align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj
 
-theorem re_eq_abs_of_mul_conj (x : K) : re (x * conj x) = abs (x * conj x) := by
-  rw [mul_conj, of_real_re, abs_of_real, norm_sq_eq_abs, sq, _root_.abs_mul, abs_abs]
-#align is_R_or_C.re_eq_abs_of_mul_conj IsROrC.re_eq_abs_of_mul_conj
+theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
+  rw [add_conj, norm_mul, norm_two, norm_of_real, two_mul (re x : K), map_add, of_real_re, ←
+    two_mul, mul_pow, mul_pow, sq_abs]
+#align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conj
 
-theorem abs_sq_re_add_conj (x : K) : abs (x + conj x) ^ 2 = re (x + conj x) ^ 2 := by
-  simp only [sq, ← norm_sq_eq_abs, norm_sq, map_add, add_zero, MonoidWithZeroHom.coe_mk,
-    add_right_neg, MulZeroClass.mul_zero, is_R_or_C_simps]
-#align is_R_or_C.abs_sq_re_add_conj IsROrC.abs_sq_re_add_conj
-
-theorem abs_sq_re_add_conj' (x : K) : abs (conj x + x) ^ 2 = re (conj x + x) ^ 2 := by
-  simp only [sq, ← norm_sq_eq_abs, norm_sq, map_add, add_zero, MonoidWithZeroHom.coe_mk,
-    add_left_neg, MulZeroClass.mul_zero, is_R_or_C_simps]
-#align is_R_or_C.abs_sq_re_add_conj' IsROrC.abs_sq_re_add_conj'
+theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2 := by
+  rw [add_comm, norm_sq_re_add_conj]
+#align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_add
 
 /-! ### Cauchy sequences -/
 
 
-theorem isCauSeq_re (f : CauSeq K abs) : IsCauSeq abs' fun n => re (f n) := fun ε ε0 =>
+theorem isCauSeq_re (f : CauSeq K norm) : IsCauSeq abs fun n => re (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
-    lt_of_le_of_lt (by simpa using abs_re_le_abs (f j - f i)) (H _ ij)
+    lt_of_le_of_lt (by simpa only [map_sub] using abs_re_le_norm (f j - f i)) (H _ ij)
 #align is_R_or_C.is_cau_seq_re IsROrC.isCauSeq_re
 
-theorem isCauSeq_im (f : CauSeq K abs) : IsCauSeq abs' fun n => im (f n) := fun ε ε0 =>
+theorem isCauSeq_im (f : CauSeq K norm) : IsCauSeq abs fun n => im (f n) := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
-    lt_of_le_of_lt (by simpa using abs_im_le_abs (f j - f i)) (H _ ij)
+    lt_of_le_of_lt (by simpa only [map_sub] using abs_im_le_norm (f j - f i)) (H _ ij)
 #align is_R_or_C.is_cau_seq_im IsROrC.isCauSeq_im
 
 /-- The real part of a K Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqRe (f : CauSeq K abs) : CauSeq ℝ abs' :=
+noncomputable def cauSeqRe (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_re f⟩
 #align is_R_or_C.cau_seq_re IsROrC.cauSeqRe
 
 /-- The imaginary part of a K Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqIm (f : CauSeq K abs) : CauSeq ℝ abs' :=
+noncomputable def cauSeqIm (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_im f⟩
 #align is_R_or_C.cau_seq_im IsROrC.cauSeqIm
 
-theorem isCauSeq_abs {f : ℕ → K} (hf : IsCauSeq abs f) : IsCauSeq abs' (abs ∘ f) := fun ε ε0 =>
+theorem isCauSeq_norm {f : ℕ → K} (hf : IsCauSeq norm f) : IsCauSeq abs (norm ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
-  ⟨i, fun j hj => lt_of_le_of_lt (abs_abs_sub_le_abs_sub _ _) (hi j hj)⟩
-#align is_R_or_C.is_cau_seq_abs IsROrC.isCauSeq_abs
+  ⟨i, fun j hj => lt_of_le_of_lt (abs_norm_sub_norm_le _ _) (hi j hj)⟩
+#align is_R_or_C.is_cau_seq_norm IsROrC.isCauSeq_norm
 
 end IsROrC
 
@@ -971,9 +826,6 @@ local notation "imR" => @IsROrC.im ℝ _
 -- mathport name: exprIR
 local notation "IR" => @IsROrC.i ℝ _
 
--- mathport name: exprabsR
-local notation "absR" => @IsROrC.abs ℝ _
-
 -- mathport name: exprnorm_sqR
 local notation "norm_sqR" => @IsROrC.normSq ℝ _
 
@@ -1001,11 +853,6 @@ theorem i_to_real : IR = 0 :=
 theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [IsROrC.normSq]
 #align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_real
 
-@[simp, is_R_or_C_simps]
-theorem abs_to_real {x : ℝ} : absR x = Abs.abs x := by
-  simp [IsROrC.abs, abs, Real.sqrt_mul_self_eq_abs]
-#align is_R_or_C.abs_to_real IsROrC.abs_to_real
-
 @[simp]
 theorem coe_real_eq_id : @coe ℝ ℝ _ = id :=
   rfl
@@ -1027,10 +874,9 @@ theorem reLm_coe : (reLm : K → ℝ) = re :=
 
 /-- The real part in a `is_R_or_C` field, as a continuous linear map. -/
 noncomputable def reClm : K →L[ℝ] ℝ :=
-  LinearMap.mkContinuous reLm 1 <|
-    by
-    simp only [norm_eq_abs, re_lm_coe, one_mul, abs_to_real]
-    exact abs_re_le_abs
+  LinearMap.mkContinuous reLm 1 fun x => by
+    rw [one_mul]
+    exact abs_re_le_norm x
 #align is_R_or_C.re_clm IsROrC.reClm
 
 @[simp, is_R_or_C_simps, norm_cast]
@@ -1060,10 +906,9 @@ theorem imLm_coe : (imLm : K → ℝ) = im :=
 
 /-- The imaginary part in a `is_R_or_C` field, as a continuous linear map. -/
 noncomputable def imClm : K →L[ℝ] ℝ :=
-  LinearMap.mkContinuous imLm 1 <|
-    by
-    simp only [norm_eq_abs, re_lm_coe, one_mul, abs_to_real]
-    exact abs_im_le_abs
+  LinearMap.mkContinuous imLm 1 fun x => by
+    rw [one_mul]
+    exact abs_im_le_norm x
 #align is_R_or_C.im_clm IsROrC.imClm
 
 @[simp, is_R_or_C_simps, norm_cast]
@@ -1097,7 +942,7 @@ theorem conjAe_coe : (conjAe : K → K) = conj :=
 
 /-- Conjugate as a linear isometry -/
 noncomputable def conjLie : K ≃ₗᵢ[ℝ] K :=
-  ⟨conjAe.toLinearEquiv, fun z => by simp [norm_eq_abs, is_R_or_C_simps]⟩
+  ⟨conjAe.toLinearEquiv, fun _ => norm_conj⟩
 #align is_R_or_C.conj_lie IsROrC.conjLie
 
 @[simp, is_R_or_C_simps]
@@ -1142,7 +987,7 @@ theorem ofRealAm_coe : (ofRealAm : ℝ → K) = coe :=
 noncomputable def ofRealLi : ℝ →ₗᵢ[ℝ] K
     where
   toLinearMap := ofRealAm.toLinearMap
-  norm_map' := by simp [norm_eq_abs]
+  norm_map' := norm_of_real
 #align is_R_or_C.of_real_li IsROrC.ofRealLi
 
 @[simp, is_R_or_C_simps]
@@ -1171,21 +1016,8 @@ theorem continuous_of_real : Continuous (coe : ℝ → K) :=
 #align is_R_or_C.continuous_of_real IsROrC.continuous_of_real
 
 @[continuity]
-theorem continuous_abs : Continuous (@IsROrC.abs K _) := by
-  simp only [show @IsROrC.abs K _ = Norm.norm by
-      ext
-      exact (norm_eq_abs _).symm,
-    continuous_norm]
-#align is_R_or_C.continuous_abs IsROrC.continuous_abs
-
-@[continuity]
-theorem continuous_normSq : Continuous (@IsROrC.normSq K _) :=
-  by
-  have : (@IsROrC.normSq K _ : K → ℝ) = fun x => IsROrC.abs x ^ 2 :=
-    by
-    ext
-    exact norm_sq_eq_abs _
-  simp only [this, continuous_abs.pow 2]
+theorem continuous_normSq : Continuous (normSq : K → ℝ) :=
+  (continuous_re.mul continuous_re).add (continuous_im.mul continuous_im)
 #align is_R_or_C.continuous_norm_sq IsROrC.continuous_normSq
 
 end LinearMaps

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit 338fe44f54751b9f7deaca47ffca3509f53140ae
+! leanprover-community/mathlib commit 25580801f04aed44a0daf912d3760d0eaaf6d1bb
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -497,6 +497,9 @@ theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
     sub_eq_neg_add, neg_zero, is_R_or_C_simps]
 #align is_R_or_C.mul_conj IsROrC.mul_conj
 
+theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
+#align is_R_or_C.conj_mul IsROrC.conj_mul
+
 theorem add_conj (z : K) : z + conj z = 2 * re z := by
   simp only [ext_iff, two_mul, map_add, add_zero, of_real_im, conj_im, of_real_re, eq_self_iff_true,
     add_right_neg, conj_re, and_self_iff]
@@ -893,17 +896,6 @@ theorem abs_sq_re_add_conj' (x : K) : abs (conj x + x) ^ 2 = re (conj x + x) ^ 2
     add_left_neg, MulZeroClass.mul_zero, is_R_or_C_simps]
 #align is_R_or_C.abs_sq_re_add_conj' IsROrC.abs_sq_re_add_conj'
 
-theorem conj_mul_eq_normSq_left (x : K) : conj x * x = (normSq x : K) :=
-  by
-  rw [ext_iff]
-  refine'
-    ⟨by
-      simp only [norm_sq, neg_mul, MonoidWithZeroHom.coe_mk, sub_neg_eq_add, map_add, sub_zero,
-        MulZeroClass.mul_zero, is_R_or_C_simps],
-      _⟩
-  simp only [mul_comm, mul_neg, add_left_neg, is_R_or_C_simps]
-#align is_R_or_C.conj_mul_eq_norm_sq_left IsROrC.conj_mul_eq_normSq_left
-
 /-! ### Cauchy sequences -/
 
 

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: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit caa58cbf5bfb7f81ccbaca4e8b8ac4bc2b39cc1c
+! leanprover-community/mathlib commit 338fe44f54751b9f7deaca47ffca3509f53140ae
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -73,8 +73,6 @@ class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebr
   conj_i_ax : conj I = -I
   norm_sq_eq_def_ax : ∀ z : K, ‖z‖ ^ 2 = re z * re z + im z * im z
   mul_im_i_ax : ∀ z : K, im z * im I = im z
-  inv_def_ax : ∀ z : K, z⁻¹ = conj z * 𝓚 (‖z‖ ^ 2)⁻¹
-  div_i_ax : ∀ z : K, z / I = -(z * I)
 #align is_R_or_C IsROrC
 
 end
@@ -102,8 +100,8 @@ theorem of_real_alg (x : ℝ) : (x : K) = x • (1 : K) :=
   Algebra.algebraMap_eq_smul_one x
 #align is_R_or_C.of_real_alg IsROrC.of_real_alg
 
-theorem real_smul_eq_coe_mul (r : ℝ) (z : K) : r • z = (r : K) * z := by
-  rw [IsROrC.of_real_alg, ← smul_eq_mul, smul_assoc, smul_eq_mul, one_mul]
+theorem real_smul_eq_coe_mul (r : ℝ) (z : K) : r • z = (r : K) * z :=
+  Algebra.smul_def r z
 #align is_R_or_C.real_smul_eq_coe_mul IsROrC.real_smul_eq_coe_mul
 
 theorem real_smul_eq_coe_smul [AddCommGroup E] [Module K E] [Module ℝ E] [IsScalarTower ℝ K E]
@@ -139,23 +137,12 @@ theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
   IsROrC.mul_im_ax
 #align is_R_or_C.mul_im IsROrC.mul_im
 
-theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
-  IsROrC.inv_def_ax z
-#align is_R_or_C.inv_def IsROrC.inv_def
-
-theorem ext_iff : ∀ {z w : K}, z = w ↔ re z = re w ∧ im z = im w := fun z w =>
-  { mp := by
-      rintro rfl
-      cc
-    mpr := by
-      rintro ⟨h₁, h₂⟩
-      rw [← re_add_im z, ← re_add_im w, h₁, h₂] }
+theorem ext_iff {z w : K} : z = w ↔ re z = re w ∧ im z = im w :=
+  ⟨fun h => h ▸ ⟨rfl, rfl⟩, fun ⟨h₁, h₂⟩ => re_add_im z ▸ re_add_im w ▸ h₁ ▸ h₂ ▸ rfl⟩
 #align is_R_or_C.ext_iff IsROrC.ext_iff
 
-theorem ext : ∀ {z w : K}, re z = re w → im z = im w → z = w :=
-  by
-  simp_rw [ext_iff]
-  cc
+theorem ext {z w : K} (hre : re z = re w) (him : im z = im w) : z = w :=
+  ext_iff.2 ⟨hre, him⟩
 #align is_R_or_C.ext IsROrC.ext
 
 @[norm_cast]
@@ -168,7 +155,8 @@ theorem zero_re' : re (0 : K) = (0 : ℝ) :=
 #align is_R_or_C.zero_re' IsROrC.zero_re'
 
 @[norm_cast]
-theorem of_real_one : ((1 : ℝ) : K) = 1 := by rw [of_real_alg, one_smul]
+theorem of_real_one : ((1 : ℝ) : K) = 1 :=
+  map_one (algebraMap ℝ K)
 #align is_R_or_C.of_real_one IsROrC.of_real_one
 
 @[simp, is_R_or_C_simps]
@@ -179,65 +167,101 @@ theorem one_re : re (1 : K) = 1 := by rw [← of_real_one, of_real_re]
 theorem one_im : im (1 : K) = 0 := by rw [← of_real_one, of_real_im]
 #align is_R_or_C.one_im IsROrC.one_im
 
+theorem of_real_injective : Function.Injective (coe : ℝ → K) :=
+  (algebraMap ℝ K).Injective
+#align is_R_or_C.of_real_injective IsROrC.of_real_injective
+
 @[norm_cast]
 theorem of_real_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
-  { mp := fun h => by convert congr_arg re h <;> simp only [of_real_re]
-    mpr := fun h => by rw [h] }
+  algebraMap.coe_inj
 #align is_R_or_C.of_real_inj IsROrC.of_real_inj
 
 @[simp, is_R_or_C_simps]
-theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) := by simp only [bit0, map_add]
+theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
+  map_bit0 _ _
 #align is_R_or_C.bit0_re IsROrC.bit0_re
 
 @[simp, is_R_or_C_simps]
-theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by
-  simp only [bit1, AddMonoidHom.map_add, bit0_re, add_right_inj, one_re]
+theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_add, bit0_re, one_re]
 #align is_R_or_C.bit1_re IsROrC.bit1_re
 
 @[simp, is_R_or_C_simps]
-theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) := by simp only [bit0, map_add]
+theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
+  map_bit0 _ _
 #align is_R_or_C.bit0_im IsROrC.bit0_im
 
 @[simp, is_R_or_C_simps]
 theorem bit1_im (z : K) : im (bit1 z) = bit0 (im z) := by
-  simp only [bit1, add_right_eq_self, AddMonoidHom.map_add, bit0_im, one_im]
+  simp only [bit1, map_add, bit0_im, one_im, add_zero]
 #align is_R_or_C.bit1_im IsROrC.bit1_im
 
-theorem of_real_eq_zero {z : ℝ} : (z : K) = 0 ↔ z = 0 := by
-  rw [← of_real_zero] <;> exact of_real_inj
+theorem of_real_eq_zero {x : ℝ} : (x : K) = 0 ↔ x = 0 :=
+  algebraMap.lift_map_eq_zero_iff x
 #align is_R_or_C.of_real_eq_zero IsROrC.of_real_eq_zero
 
-theorem of_real_ne_zero {z : ℝ} : (z : K) ≠ 0 ↔ z ≠ 0 :=
+theorem of_real_ne_zero {x : ℝ} : (x : K) ≠ 0 ↔ x ≠ 0 :=
   of_real_eq_zero.Not
 #align is_R_or_C.of_real_ne_zero IsROrC.of_real_ne_zero
 
 @[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_add ⦃r s : ℝ⦄ : ((r + s : ℝ) : K) = r + s :=
-  by
-  apply (@IsROrC.ext_iff K _ ((r + s : ℝ) : K) (r + s)).mpr
-  simp
+theorem of_real_add (r s : ℝ) : ((r + s : ℝ) : K) = r + s :=
+  algebraMap.coe_add _ _
 #align is_R_or_C.of_real_add IsROrC.of_real_add
 
 @[simp, is_R_or_C_simps, norm_cast]
 theorem of_real_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
-  ext_iff.2 <| by simp [bit0]
+  of_real_add _ _
 #align is_R_or_C.of_real_bit0 IsROrC.of_real_bit0
 
 @[simp, is_R_or_C_simps, norm_cast]
 theorem of_real_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
-  ext_iff.2 <| by simp [bit1]
+  map_bit1 (algebraMap ℝ K) r
 #align is_R_or_C.of_real_bit1 IsROrC.of_real_bit1
 
 @[simp, norm_cast, is_R_or_C_simps]
 theorem of_real_neg (r : ℝ) : ((-r : ℝ) : K) = -r :=
-  ext_iff.2 <| by simp
+  algebraMap.coe_neg r
 #align is_R_or_C.of_real_neg IsROrC.of_real_neg
 
+@[simp, norm_cast, is_R_or_C_simps]
+theorem of_real_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
+  map_sub (algebraMap ℝ K) r s
+#align is_R_or_C.of_real_sub IsROrC.of_real_sub
+
+@[simp, is_R_or_C_simps, norm_cast]
+theorem of_real_sum {α : Type _} (s : Finset α) (f : α → ℝ) :
+    ((∑ i in s, f i : ℝ) : K) = ∑ i in s, (f i : K) :=
+  map_sum (algebraMap ℝ K) _ _
+#align is_R_or_C.of_real_sum IsROrC.of_real_sum
+
+@[simp, is_R_or_C_simps, norm_cast]
+theorem of_real_finsupp_sum {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
+    ((f.Sum fun a b => g a b : ℝ) : K) = f.Sum fun a b => (g a b : K) :=
+  map_finsupp_sum (algebraMap ℝ K) f g
+#align is_R_or_C.of_real_finsupp_sum IsROrC.of_real_finsupp_sum
+
 @[simp, norm_cast, is_R_or_C_simps]
 theorem of_real_mul (r s : ℝ) : ((r * s : ℝ) : K) = r * s :=
-  ext_iff.2 <| by simp [is_R_or_C_simps]
+  algebraMap.coe_mul _ _
 #align is_R_or_C.of_real_mul IsROrC.of_real_mul
 
+@[simp, norm_cast, is_R_or_C_simps]
+theorem of_real_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
+  map_pow (algebraMap ℝ K) r n
+#align is_R_or_C.of_real_pow IsROrC.of_real_pow
+
+@[simp, is_R_or_C_simps, norm_cast]
+theorem of_real_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
+    ((∏ i in s, f i : ℝ) : K) = ∏ i in s, (f i : K) :=
+  RingHom.map_prod _ _ _
+#align is_R_or_C.of_real_prod IsROrC.of_real_prod
+
+@[simp, is_R_or_C_simps, norm_cast]
+theorem of_real_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
+    ((f.Prod fun a b => g a b : ℝ) : K) = f.Prod fun a b => (g a b : K) :=
+  RingHom.map_finsupp_prod _ f g
+#align is_R_or_C.of_real_finsupp_prod IsROrC.of_real_finsupp_prod
+
 @[simp, norm_cast, is_R_or_C_simps]
 theorem of_real_smul (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
   by
@@ -324,19 +348,17 @@ theorem conj_of_real (r : ℝ) : conj (r : K) = (r : K) :=
 #align is_R_or_C.conj_of_real IsROrC.conj_of_real
 
 @[simp, is_R_or_C_simps]
-theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) := by
-  simp only [bit0, RingHom.map_add, eq_self_iff_true]
+theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
+  map_bit0 _ _
 #align is_R_or_C.conj_bit0 IsROrC.conj_bit0
 
 @[simp, is_R_or_C_simps]
-theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) := by
-  simp only [bit0, ext_iff, bit1_re, conj_im, eq_self_iff_true, conj_re, neg_add_rev, and_self_iff,
-    bit1_im]
+theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
+  map_bit1 _ _
 #align is_R_or_C.conj_bit1 IsROrC.conj_bit1
 
 @[simp, is_R_or_C_simps]
-theorem conj_neg_i : conj (-i) = (i : K) := by
-  simp only [conj_I, RingHom.map_neg, eq_self_iff_true, neg_neg]
+theorem conj_neg_i : conj (-i) = (i : K) := by rw [map_neg, conj_I, neg_neg]
 #align is_R_or_C.conj_neg_I IsROrC.conj_neg_i
 
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
@@ -480,30 +502,6 @@ theorem add_conj (z : K) : z + conj z = 2 * re z := by
     add_right_neg, conj_re, and_self_iff]
 #align is_R_or_C.add_conj IsROrC.add_conj
 
-/-- The pseudo-coercion `of_real` as a `ring_hom`. -/
-noncomputable def ofRealHom : ℝ →+* K :=
-  algebraMap ℝ K
-#align is_R_or_C.of_real_hom IsROrC.ofRealHom
-
-/-- The coercion from reals as a `ring_hom`. -/
-noncomputable def coeHom : ℝ →+* K :=
-  ⟨coe, of_real_one, of_real_mul, of_real_zero, of_real_add⟩
-#align is_R_or_C.coe_hom IsROrC.coeHom
-
-@[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
-  ext_iff.2 <| by
-    simp only [of_real_im, of_real_re, eq_self_iff_true, sub_zero, and_self_iff, map_sub]
-#align is_R_or_C.of_real_sub IsROrC.of_real_sub
-
-@[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
-  by
-  induction n
-  · simp only [of_real_one, pow_zero]
-  · simp only [*, of_real_mul, pow_succ]
-#align is_R_or_C.of_real_pow IsROrC.of_real_pow
-
 theorem sub_conj (z : K) : z - conj z = 2 * im z * i := by
   simp only [ext_iff, two_mul, sub_eq_add_neg, add_mul, map_add, add_zero, add_left_inj,
     MulZeroClass.zero_mul, map_add_neg, eq_self_iff_true, add_right_neg, and_self_iff, neg_neg,
@@ -514,46 +512,37 @@ theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z
   simp only [norm_sq_add, sub_eq_add_neg, RingEquiv.map_neg, mul_neg, norm_sq_neg, map_neg]
 #align is_R_or_C.norm_sq_sub IsROrC.normSq_sub
 
-theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ :=
-  by
-  have h₂ : ‖z‖ = Real.sqrt (‖z‖ ^ 2) := (Real.sqrt_sq (norm_nonneg z)).symm
-  rw [h₂]
-  exact congr_arg Real.sqrt (norm_sq_eq_def' z)
+theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
+  rw [norm_sq_eq_def', Real.sqrt_sq (norm_nonneg _)]
 #align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_norm
 
 /-! ### Inversion -/
 
 
+@[simp, norm_cast, is_R_or_C_simps]
+theorem of_real_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = r⁻¹ :=
+  map_inv₀ (algebraMap ℝ K) r
+#align is_R_or_C.of_real_inv IsROrC.of_real_inv
+
+theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) :=
+  by
+  rcases eq_or_ne z 0 with (rfl | h₀)
+  · simp
+  · apply inv_eq_of_mul_eq_one_right
+    rw [← mul_assoc, mul_conj, of_real_inv, ← norm_sq_eq_def', mul_inv_cancel]
+    rwa [of_real_ne_zero, Ne.def, norm_sq_eq_zero]
+#align is_R_or_C.inv_def IsROrC.inv_def
+
 @[simp, is_R_or_C_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
-  simp only [inv_def, norm_sq_eq_def, norm_sq, division_def, MonoidWithZeroHom.coe_mk, sub_zero,
-    MulZeroClass.mul_zero, is_R_or_C_simps]
+  rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_re, conj_re, div_eq_inv_mul]
 #align is_R_or_C.inv_re IsROrC.inv_re
 
 @[simp, is_R_or_C_simps]
-theorem inv_im (z : K) : im z⁻¹ = im (-z) / normSq z := by
-  simp only [inv_def, norm_sq_eq_def, norm_sq, division_def, of_real_im, MonoidWithZeroHom.coe_mk,
-    of_real_re, zero_add, map_neg, MulZeroClass.mul_zero, is_R_or_C_simps]
+theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
+  rw [inv_def, norm_sq_eq_def', mul_comm, of_real_mul_im, conj_im, div_eq_inv_mul]
 #align is_R_or_C.inv_im IsROrC.inv_im
 
-@[simp, norm_cast, is_R_or_C_simps]
-theorem of_real_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = r⁻¹ :=
-  by
-  rw [ext_iff]
-  by_cases r = 0
-  · simp only [h, of_real_zero, inv_zero, and_self_iff, map_zero]
-  · simp only [is_R_or_C_simps]
-    field_simp [h, norm_sq]
-#align is_R_or_C.of_real_inv IsROrC.of_real_inv
-
-protected theorem inv_zero : (0⁻¹ : K) = 0 := by rw [← of_real_zero, ← of_real_inv, inv_zero]
-#align is_R_or_C.inv_zero IsROrC.inv_zero
-
-protected theorem mul_inv_cancel {z : K} (h : z ≠ 0) : z * z⁻¹ = 1 := by
-  rw [inv_def, ← mul_assoc, mul_conj, ← of_real_mul, ← norm_sq_eq_def',
-    mul_inv_cancel (mt norm_sq_eq_zero.1 h), of_real_one]
-#align is_R_or_C.mul_inv_cancel IsROrC.mul_inv_cancel
-
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, neg_mul, mul_neg, neg_neg, map_neg,
     is_R_or_C_simps]
@@ -571,27 +560,20 @@ theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
 
 @[simp, norm_cast, is_R_or_C_simps]
 theorem of_real_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
-  map_div₀ (@IsROrC.coeHom K _) r s
+  map_div₀ (algebraMap ℝ K) r s
 #align is_R_or_C.of_real_div IsROrC.of_real_div
 
-theorem div_re_of_real {z : K} {r : ℝ} : re (z / r) = re z / r :=
-  by
-  by_cases h : r = 0
-  · simp only [h, of_real_zero, div_zero, zero_re']
-  · change r ≠ 0 at h
-    rw [div_eq_mul_inv, ← of_real_inv, div_eq_mul_inv]
-    simp only [one_div, of_real_im, of_real_re, sub_zero, mul_re, MulZeroClass.mul_zero]
+theorem div_re_of_real {z : K} {r : ℝ} : re (z / r) = re z / r := by
+  rw [div_eq_inv_mul, div_eq_inv_mul, ← of_real_inv, of_real_mul_re]
 #align is_R_or_C.div_re_of_real IsROrC.div_re_of_real
 
 @[simp, norm_cast, is_R_or_C_simps]
 theorem of_real_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : K) = r ^ n :=
-  map_zpow₀ (@IsROrC.coeHom K _) r n
+  map_zpow₀ (algebraMap ℝ K) r n
 #align is_R_or_C.of_real_zpow IsROrC.of_real_zpow
 
 theorem i_mul_i_of_nonzero : (i : K) ≠ 0 → (i : K) * i = -1 :=
-  by
-  have := I_mul_I_ax
-  tauto
+  i_mul_i_ax.resolve_left
 #align is_R_or_C.I_mul_I_of_nonzero IsROrC.i_mul_i_of_nonzero
 
 @[simp, is_R_or_C_simps]
@@ -628,7 +610,7 @@ instance (priority := 100) : CstarRing K
 
 @[simp, is_R_or_C_simps, norm_cast]
 theorem of_real_nat_cast (n : ℕ) : ((n : ℝ) : K) = n :=
-  map_natCast (@ofRealHom K _) n
+  map_natCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_nat_cast IsROrC.of_real_nat_cast
 
 @[simp, is_R_or_C_simps, norm_cast]
@@ -641,7 +623,7 @@ theorem nat_cast_im (n : ℕ) : im (n : K) = 0 := by rw [← of_real_nat_cast, o
 
 @[simp, is_R_or_C_simps, norm_cast]
 theorem of_real_int_cast (n : ℤ) : ((n : ℝ) : K) = n :=
-  map_intCast (@ofRealHom K _) n
+  map_intCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_int_cast IsROrC.of_real_int_cast
 
 @[simp, is_R_or_C_simps, norm_cast]
@@ -654,7 +636,7 @@ theorem int_cast_im (n : ℤ) : im (n : K) = 0 := by rw [← of_real_int_cast, o
 
 @[simp, is_R_or_C_simps, norm_cast]
 theorem of_real_rat_cast (n : ℚ) : ((n : ℝ) : K) = n :=
-  map_ratCast (@IsROrC.ofRealHom K _) n
+  map_ratCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_rat_cast IsROrC.of_real_rat_cast
 
 @[simp, is_R_or_C_simps, norm_cast]
@@ -950,30 +932,6 @@ theorem isCauSeq_abs {f : ℕ → K} (hf : IsCauSeq abs f) : IsCauSeq abs' (abs
   ⟨i, fun j hj => lt_of_le_of_lt (abs_abs_sub_le_abs_sub _ _) (hi j hj)⟩
 #align is_R_or_C.is_cau_seq_abs IsROrC.isCauSeq_abs
 
-@[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
-    ((∏ i in s, f i : ℝ) : K) = ∏ i in s, (f i : K) :=
-  RingHom.map_prod _ _ _
-#align is_R_or_C.of_real_prod IsROrC.of_real_prod
-
-@[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_sum {α : Type _} (s : Finset α) (f : α → ℝ) :
-    ((∑ i in s, f i : ℝ) : K) = ∑ i in s, (f i : K) :=
-  RingHom.map_sum _ _ _
-#align is_R_or_C.of_real_sum IsROrC.of_real_sum
-
-@[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_finsupp_sum {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
-    ((f.Sum fun a b => g a b : ℝ) : K) = f.Sum fun a b => (g a b : K) :=
-  RingHom.map_finsupp_sum _ f g
-#align is_R_or_C.of_real_finsupp_sum IsROrC.of_real_finsupp_sum
-
-@[simp, is_R_or_C_simps, norm_cast]
-theorem of_real_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
-    ((f.Prod fun a b => g a b : ℝ) : K) = f.Prod fun a b => (g a b : K) :=
-  RingHom.map_finsupp_prod _ f g
-#align is_R_or_C.of_real_finsupp_prod IsROrC.of_real_finsupp_prod
-
 end IsROrC
 
 section Instances
@@ -1001,11 +959,7 @@ noncomputable instance Real.isROrC : IsROrC ℝ :=
     norm_sq_eq_def_ax := fun z => by
       simp only [sq, Real.norm_eq_abs, ← abs_mul, abs_mul_self z, add_zero, MulZeroClass.mul_zero,
         AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
-    mul_im_i_ax := fun z => by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply]
-    inv_def_ax := fun z => by
-      simp only [starRingEnd_apply, star, sq, Real.norm_eq_abs, abs_mul_abs_self, ← div_eq_mul_inv,
-        Algebra.id.map_eq_id, id.def, RingHom.id_apply, div_self_mul_self']
-    div_i_ax := fun z => by simp only [div_zero, MulZeroClass.mul_zero, neg_zero] }
+    mul_im_i_ax := fun z => by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply] }
 #align real.is_R_or_C Real.isROrC
 
 end Instances

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit 468b141b14016d54b479eb7a0fff1e360b7e3cf6
+! leanprover-community/mathlib commit caa58cbf5bfb7f81ccbaca4e8b8ac4bc2b39cc1c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -357,7 +357,7 @@ theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z :=
   simp only [one_mul, Algebra.smul_mul_assoc]
 #align is_R_or_C.conj_smul IsROrC.conj_smul
 
-theorem eq_conj_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
+theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
   by
   constructor
   · intro h
@@ -373,7 +373,7 @@ theorem eq_conj_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
     simpa [neg_eq_iff_add_eq_zero, add_self_eq_zero]
   · rintro ⟨r, rfl⟩
     apply conj_of_real
-#align is_R_or_C.eq_conj_iff_real IsROrC.eq_conj_iff_real
+#align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_real
 
 @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
@@ -390,9 +390,9 @@ abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
 
 variable {K}
 
-theorem eq_conj_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
-  eq_conj_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
-#align is_R_or_C.eq_conj_iff_re IsROrC.eq_conj_iff_re
+theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
+  conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
+#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
 
 /-- The norm squared function. -/
 def normSq : K →*₀ ℝ where

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

@@ -364,7 +364,7 @@ theorem eq_conj_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
     suffices im z = 0 by
       use re z
       rw [← add_zero (coe _)]
-      convert (re_add_im z).symm
+      convert(re_add_im z).symm
       simp [this]
     contrapose! h
     rw [← re_add_im z]

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

@@ -247,12 +247,12 @@ theorem of_real_smul (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
 
 @[is_R_or_C_simps]
 theorem of_real_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
-  simp only [mul_re, of_real_im, zero_mul, of_real_re, sub_zero]
+  simp only [mul_re, of_real_im, MulZeroClass.zero_mul, of_real_re, sub_zero]
 #align is_R_or_C.of_real_mul_re IsROrC.of_real_mul_re
 
 @[is_R_or_C_simps]
 theorem of_real_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
-  simp only [add_zero, of_real_im, zero_mul, of_real_re, mul_im]
+  simp only [add_zero, of_real_im, MulZeroClass.zero_mul, of_real_re, mul_im]
 #align is_R_or_C.of_real_mul_im IsROrC.of_real_mul_im
 
 @[is_R_or_C_simps]
@@ -294,7 +294,7 @@ theorem i_im' (z : K) : im (i : K) * im z = im z := by rw [mul_comm, I_im _]
 
 @[simp, is_R_or_C_simps]
 theorem i_mul_re (z : K) : re (i * z) = -im z := by
-  simp only [I_re, zero_sub, I_im', zero_mul, mul_re]
+  simp only [I_re, zero_sub, I_im', MulZeroClass.zero_mul, mul_re]
 #align is_R_or_C.I_mul_re IsROrC.i_mul_re
 
 theorem i_mul_i : (i : K) = 0 ∨ (i : K) * i = -1 :=
@@ -342,8 +342,9 @@ theorem conj_neg_i : conj (-i) = (i : K) := by
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * i :=
   by
   rw [ext_iff]
-  simp only [add_zero, I_re, of_real_im, I_im, zero_sub, zero_mul, conj_im, of_real_re,
-    eq_self_iff_true, sub_zero, conj_re, mul_im, neg_inj, and_self_iff, mul_re, mul_zero, map_sub]
+  simp only [add_zero, I_re, of_real_im, I_im, zero_sub, MulZeroClass.zero_mul, conj_im, of_real_re,
+    eq_self_iff_true, sub_zero, conj_re, mul_im, neg_inj, and_self_iff, mul_re,
+    MulZeroClass.mul_zero, map_sub]
 #align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_im
 
 @[is_R_or_C_simps]
@@ -396,8 +397,8 @@ theorem eq_conj_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
 /-- The norm squared function. -/
 def normSq : K →*₀ ℝ where
   toFun z := re z * re z + im z * im z
-  map_zero' := by simp only [add_zero, mul_zero, map_zero]
-  map_one' := by simp only [one_im, add_zero, mul_one, one_re, mul_zero]
+  map_zero' := by simp only [add_zero, MulZeroClass.mul_zero, map_zero]
+  map_one' := by simp only [one_im, add_zero, mul_one, one_re, MulZeroClass.mul_zero]
   map_mul' z w := by
     simp only [mul_im, mul_re]
     ring
@@ -469,9 +470,9 @@ theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
 
 theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
   simp only [map_add, add_zero, ext_iff, MonoidWithZeroHom.coe_mk, add_left_inj,
-    mul_eq_mul_left_iff, zero_mul, add_comm, true_or_iff, eq_self_iff_true, mul_neg, add_right_neg,
-    zero_add, norm_sq, mul_comm, and_self_iff, neg_neg, mul_zero, sub_eq_neg_add, neg_zero,
-    is_R_or_C_simps]
+    mul_eq_mul_left_iff, MulZeroClass.zero_mul, add_comm, true_or_iff, eq_self_iff_true, mul_neg,
+    add_right_neg, zero_add, norm_sq, mul_comm, and_self_iff, neg_neg, MulZeroClass.mul_zero,
+    sub_eq_neg_add, neg_zero, is_R_or_C_simps]
 #align is_R_or_C.mul_conj IsROrC.mul_conj
 
 theorem add_conj (z : K) : z + conj z = 2 * re z := by
@@ -504,9 +505,9 @@ theorem of_real_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = r ^ n :=
 #align is_R_or_C.of_real_pow IsROrC.of_real_pow
 
 theorem sub_conj (z : K) : z - conj z = 2 * im z * i := by
-  simp only [ext_iff, two_mul, sub_eq_add_neg, add_mul, map_add, add_zero, add_left_inj, zero_mul,
-    map_add_neg, eq_self_iff_true, add_right_neg, and_self_iff, neg_neg, mul_zero, neg_zero,
-    is_R_or_C_simps]
+  simp only [ext_iff, two_mul, sub_eq_add_neg, add_mul, map_add, add_zero, add_left_inj,
+    MulZeroClass.zero_mul, map_add_neg, eq_self_iff_true, add_right_neg, and_self_iff, neg_neg,
+    MulZeroClass.mul_zero, neg_zero, is_R_or_C_simps]
 #align is_R_or_C.sub_conj IsROrC.sub_conj
 
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
@@ -526,13 +527,13 @@ theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ :=
 @[simp, is_R_or_C_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
   simp only [inv_def, norm_sq_eq_def, norm_sq, division_def, MonoidWithZeroHom.coe_mk, sub_zero,
-    mul_zero, is_R_or_C_simps]
+    MulZeroClass.mul_zero, is_R_or_C_simps]
 #align is_R_or_C.inv_re IsROrC.inv_re
 
 @[simp, is_R_or_C_simps]
 theorem inv_im (z : K) : im z⁻¹ = im (-z) / normSq z := by
   simp only [inv_def, norm_sq_eq_def, norm_sq, division_def, of_real_im, MonoidWithZeroHom.coe_mk,
-    of_real_re, zero_add, map_neg, mul_zero, is_R_or_C_simps]
+    of_real_re, zero_add, map_neg, MulZeroClass.mul_zero, is_R_or_C_simps]
 #align is_R_or_C.inv_im IsROrC.inv_im
 
 @[simp, norm_cast, is_R_or_C_simps]
@@ -579,7 +580,7 @@ theorem div_re_of_real {z : K} {r : ℝ} : re (z / r) = re z / r :=
   · simp only [h, of_real_zero, div_zero, zero_re']
   · change r ≠ 0 at h
     rw [div_eq_mul_inv, ← of_real_inv, div_eq_mul_inv]
-    simp only [one_div, of_real_im, of_real_re, sub_zero, mul_re, mul_zero]
+    simp only [one_div, of_real_im, of_real_re, sub_zero, mul_re, MulZeroClass.mul_zero]
 #align is_R_or_C.div_re_of_real IsROrC.div_re_of_real
 
 @[simp, norm_cast, is_R_or_C_simps]
@@ -703,7 +704,7 @@ local notation "absK" => @abs K _
 @[simp, norm_cast]
 theorem abs_of_real (r : ℝ) : absK r = abs' r := by
   simp only [abs, norm_sq, Real.sqrt_mul_self_eq_abs, add_zero, of_real_im,
-    MonoidWithZeroHom.coe_mk, of_real_re, mul_zero]
+    MonoidWithZeroHom.coe_mk, of_real_re, MulZeroClass.mul_zero]
 #align is_R_or_C.abs_of_real IsROrC.abs_of_real
 
 theorem norm_eq_abs (z : K) : ‖z‖ = absK z := by
@@ -816,7 +817,8 @@ theorem im_eq_zero_of_le {a : K} (h : abs a ≤ re a) : im a = 0 :=
 theorem re_eq_self_of_le {a : K} (h : abs a ≤ re a) : (re a : K) = a :=
   by
   rw [← re_add_im a]
-  simp only [im_eq_zero_of_le h, add_zero, zero_mul, algebraMap.coe_zero, is_R_or_C_simps]
+  simp only [im_eq_zero_of_le h, add_zero, MulZeroClass.zero_mul, algebraMap.coe_zero,
+    is_R_or_C_simps]
 #align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_le
 
 theorem abs_add (z w : K) : abs (z + w) ≤ abs z + abs w :=
@@ -901,12 +903,12 @@ theorem re_eq_abs_of_mul_conj (x : K) : re (x * conj x) = abs (x * conj x) := by
 
 theorem abs_sq_re_add_conj (x : K) : abs (x + conj x) ^ 2 = re (x + conj x) ^ 2 := by
   simp only [sq, ← norm_sq_eq_abs, norm_sq, map_add, add_zero, MonoidWithZeroHom.coe_mk,
-    add_right_neg, mul_zero, is_R_or_C_simps]
+    add_right_neg, MulZeroClass.mul_zero, is_R_or_C_simps]
 #align is_R_or_C.abs_sq_re_add_conj IsROrC.abs_sq_re_add_conj
 
 theorem abs_sq_re_add_conj' (x : K) : abs (conj x + x) ^ 2 = re (conj x + x) ^ 2 := by
   simp only [sq, ← norm_sq_eq_abs, norm_sq, map_add, add_zero, MonoidWithZeroHom.coe_mk,
-    add_left_neg, mul_zero, is_R_or_C_simps]
+    add_left_neg, MulZeroClass.mul_zero, is_R_or_C_simps]
 #align is_R_or_C.abs_sq_re_add_conj' IsROrC.abs_sq_re_add_conj'
 
 theorem conj_mul_eq_normSq_left (x : K) : conj x * x = (normSq x : K) :=
@@ -915,7 +917,7 @@ theorem conj_mul_eq_normSq_left (x : K) : conj x * x = (normSq x : K) :=
   refine'
     ⟨by
       simp only [norm_sq, neg_mul, MonoidWithZeroHom.coe_mk, sub_neg_eq_add, map_add, sub_zero,
-        mul_zero, is_R_or_C_simps],
+        MulZeroClass.mul_zero, is_R_or_C_simps],
       _⟩
   simp only [mul_comm, mul_neg, add_left_neg, is_R_or_C_simps]
 #align is_R_or_C.conj_mul_eq_norm_sq_left IsROrC.conj_mul_eq_normSq_left
@@ -985,23 +987,25 @@ noncomputable instance Real.isROrC : IsROrC ℝ :=
     i_re_ax := by simp only [AddMonoidHom.map_zero]
     i_mul_i_ax := Or.intro_left _ rfl
     re_add_im_ax := fun z => by
-      simp only [add_zero, mul_zero, Algebra.id.map_eq_id, RingHom.id_apply, AddMonoidHom.id_apply]
+      simp only [add_zero, MulZeroClass.mul_zero, Algebra.id.map_eq_id, RingHom.id_apply,
+        AddMonoidHom.id_apply]
     of_real_re_ax := fun r => by simp only [AddMonoidHom.id_apply, Algebra.id.map_eq_self]
     of_real_im_ax := fun r => by simp only [AddMonoidHom.zero_apply]
     mul_re_ax := fun z w => by
-      simp only [sub_zero, mul_zero, AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
-    mul_im_ax := fun z w => by simp only [add_zero, zero_mul, mul_zero, AddMonoidHom.zero_apply]
+      simp only [sub_zero, MulZeroClass.mul_zero, AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
+    mul_im_ax := fun z w => by
+      simp only [add_zero, MulZeroClass.zero_mul, MulZeroClass.mul_zero, AddMonoidHom.zero_apply]
     conj_re_ax := fun z => by simp only [starRingEnd_apply, star_id_of_comm]
     conj_im_ax := fun z => by simp only [neg_zero, AddMonoidHom.zero_apply]
     conj_i_ax := by simp only [RingHom.map_zero, neg_zero]
     norm_sq_eq_def_ax := fun z => by
-      simp only [sq, Real.norm_eq_abs, ← abs_mul, abs_mul_self z, add_zero, mul_zero,
+      simp only [sq, Real.norm_eq_abs, ← abs_mul, abs_mul_self z, add_zero, MulZeroClass.mul_zero,
         AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
-    mul_im_i_ax := fun z => by simp only [mul_zero, AddMonoidHom.zero_apply]
+    mul_im_i_ax := fun z => by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply]
     inv_def_ax := fun z => by
       simp only [starRingEnd_apply, star, sq, Real.norm_eq_abs, abs_mul_abs_self, ← div_eq_mul_inv,
         Algebra.id.map_eq_id, id.def, RingHom.id_apply, div_self_mul_self']
-    div_i_ax := fun z => by simp only [div_zero, mul_zero, neg_zero] }
+    div_i_ax := fun z => by simp only [div_zero, MulZeroClass.mul_zero, neg_zero] }
 #align real.is_R_or_C Real.isROrC
 
 end Instances

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

@@ -1222,7 +1222,7 @@ theorem continuous_of_real : Continuous (coe : ℝ → K) :=
 
 @[continuity]
 theorem continuous_abs : Continuous (@IsROrC.abs K _) := by
-  simp only [show @IsROrC.abs K _ = HasNorm.norm by
+  simp only [show @IsROrC.abs K _ = Norm.norm by
       ext
       exact (norm_eq_abs _).symm,
     continuous_norm]

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

@@ -876,6 +876,19 @@ lemma nonpos_iff_exists_ofReal : z ≤ 0 ↔ ∃ x ≤ (0 : ℝ), x = z := by
 lemma neg_iff_exists_ofReal : z < 0 ↔ ∃ x < (0 : ℝ), x = z := by
   simp_rw [neg_iff (K := K), ext_iff (K := K)]; aesop
 
+@[simp]
+lemma ofReal_le_ofReal {x y : ℝ} : (x : K) ≤ (y : K) ↔ x ≤ y := by
+  rw [le_iff_re_im]
+  simp
+
+@[simp]
+lemma ofReal_nonneg {x : ℝ} : 0 ≤ (x : K) ↔ 0 ≤ x := by
+  rw [← ofReal_zero, ofReal_le_ofReal]
+
+@[simp]
+lemma ofReal_nonpos {x : ℝ} : (x : K) ≤ 0 ↔ x ≤ 0 := by
+  rw [← ofReal_zero, ofReal_le_ofReal]
+
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℝ` and `ℂ` are star ordered rings.
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 

@@ -987,7 +987,7 @@ theorem reCLM_apply : ((reCLM : K →L[ℝ] ℝ) : K → ℝ) = re :=
   rfl
 #align is_R_or_C.re_clm_apply RCLike.reCLM_apply
 
-@[continuity]
+@[continuity, fun_prop]
 theorem continuous_re : Continuous (re : K → ℝ) :=
   reCLM.continuous
 #align is_R_or_C.continuous_re RCLike.continuous_re
@@ -1019,7 +1019,7 @@ theorem imCLM_apply : ((imCLM : K →L[ℝ] ℝ) : K → ℝ) = im :=
   rfl
 #align is_R_or_C.im_clm_apply RCLike.imCLM_apply
 
-@[continuity]
+@[continuity, fun_prop]
 theorem continuous_im : Continuous (im : K → ℝ) :=
   imCLM.continuous
 #align is_R_or_C.continuous_im RCLike.continuous_im

StarOrderedRing was recently turned into a Prop mixin. This renames the convenience constructors to adhere to the naming convention for theorems vs. defs.

@@ -881,7 +881,7 @@ lemma neg_iff_exists_ofReal : z < 0 ↔ ∃ x < (0 : ℝ), x = z := by
 
 Note this is only an instance with `open scoped ComplexOrder`. -/
 lemma toStarOrderedRing : StarOrderedRing K :=
-  StarOrderedRing.ofNonnegIff'
+  StarOrderedRing.of_nonneg_iff'
     (h_add := fun {x y} hxy z => by
       rw [RCLike.le_iff_re_im] at *
       simpa [map_add, add_le_add_iff_left, add_right_inj] using hxy)

and reduce its scope in a few other instances. Mostly in CategoryTheory and Data this time; some Combinatorics also.

Co-authored-by: Richard Osborn <richardosborn@mac.com>

@@ -40,9 +40,6 @@ their counterparts in `Mathlib/Analysis/Complex/Basic.lean` (which causes linter
 A few lemmas requiring heavier imports are in `Mathlib/Data/RCLike/Lemmas.lean`.
 -/
 
-set_option autoImplicit true
-
-
 open BigOperators
 
 section
@@ -74,7 +71,7 @@ class RCLike (K : semiOutParam (Type*)) extends DenselyNormedField K, StarRing K
   mul_im_I_ax : ∀ z : K, im z * im I = im z
   /-- only an instance in the `ComplexOrder` locale -/
   [toPartialOrder : PartialOrder K]
-  le_iff_re_im : z ≤ w ↔ re z ≤ re w ∧ im z = im w
+  le_iff_re_im {z w : K} : z ≤ w ↔ re z ≤ re w ∧ im z = im w
   -- note we cannot put this in the `extends` clause
   [toDecidableEq : DecidableEq K]
 #align is_R_or_C RCLike

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>

@@ -521,7 +521,7 @@ theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z
   simp only [normSq_add, sub_eq_add_neg, map_neg, mul_neg, normSq_neg, map_neg]
 #align is_R_or_C.norm_sq_sub RCLike.normSq_sub
 
-theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
+theorem sqrt_normSq_eq_norm {z : K} : √(normSq z) = ‖z‖ := by
   rw [normSq_eq_def', Real.sqrt_sq (norm_nonneg _)]
 #align is_R_or_C.sqrt_norm_sq_eq_norm RCLike.sqrt_normSq_eq_norm
 
@@ -890,7 +890,7 @@ lemma toStarOrderedRing : StarOrderedRing K :=
       simpa [map_add, add_le_add_iff_left, add_right_inj] using hxy)
     (h_nonneg_iff := fun x => by
       rw [nonneg_iff]
-      refine ⟨fun h ↦ ⟨(re x).sqrt, by simp [ext_iff (K := K), h.1, h.2]⟩, ?_⟩
+      refine ⟨fun h ↦ ⟨√(re x), by simp [ext_iff (K := K), h.1, h.2]⟩, ?_⟩
       rintro ⟨s, rfl⟩
       simp [mul_comm, mul_self_nonneg, add_nonneg])
 

This makes StarOrderedRing take StarRing as a parameter instead of extending it, and as a result moves the typeclass to Prop. It was already a mixin with respect to the order and algebraic structure. There are two primary motivations:

1. This makes it possible to directly assume that C(α, R) is a StarOrderedRing with [StarOrderedRing C(α, R)], as currently there is no typeclass on R which would naturally guarantee this property. This is relevant as we want this type class on continuous functions for the continuous functional calculus.
2. We will eventually want a StarOrderedRing instance on C(α, A) where A is a complex (or even real) C⋆-algebra, and making this a mixin avoids loops with StarRing.

@@ -883,7 +883,7 @@ lemma neg_iff_exists_ofReal : z < 0 ↔ ∃ x < (0 : ℝ), x = z := by
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 
 Note this is only an instance with `open scoped ComplexOrder`. -/
-def toStarOrderedRing : StarOrderedRing K :=
+lemma toStarOrderedRing : StarOrderedRing K :=
   StarOrderedRing.ofNonnegIff'
     (h_add := fun {x y} hxy z => by
       rw [RCLike.le_iff_re_im] at *

These were interesting when they worked on number literals, which is no longer the case in lean4.

@@ -180,28 +180,12 @@ theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
   algebraMap.coe_inj
 #align is_R_or_C.of_real_inj RCLike.ofReal_inj
 
-set_option linter.deprecated false in
-@[deprecated, rclike_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
-theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
-  map_bit0 _ _
-#align is_R_or_C.bit0_re RCLike.bit0_re
-
-set_option linter.deprecated false in
-@[deprecated, simp, rclike_simps]
-theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_add, bit0_re, one_re]
-#align is_R_or_C.bit1_re RCLike.bit1_re
-
-set_option linter.deprecated false in
-@[deprecated, rclike_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
-theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
-  map_bit0 _ _
-#align is_R_or_C.bit0_im RCLike.bit0_im
-
-set_option linter.deprecated false in
-@[deprecated, simp, rclike_simps]
-theorem bit1_im (z : K) : im (bit1 z) = bit0 (im z) := by
-  simp only [bit1, map_add, bit0_im, one_im, add_zero]
-#align is_R_or_C.bit1_im RCLike.bit1_im
+-- replaced by `RCLike.ofNat_re`
+#noalign is_R_or_C.bit0_re
+#noalign is_R_or_C.bit1_re
+-- replaced by `RCLike.ofNat_im`
+#noalign is_R_or_C.bit0_im
+#noalign is_R_or_C.bit1_im
 
 theorem ofReal_eq_zero {x : ℝ} : (x : K) = 0 ↔ x = 0 :=
   algebraMap.lift_map_eq_zero_iff x
@@ -216,17 +200,9 @@ theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : K) = r + s :=
   algebraMap.coe_add _ _
 #align is_R_or_C.of_real_add RCLike.ofReal_add
 
-set_option linter.deprecated false in
-@[deprecated, simp, rclike_simps, norm_cast]
-theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
-  ofReal_add _ _
-#align is_R_or_C.of_real_bit0 RCLike.ofReal_bit0
-
-set_option linter.deprecated false in
-@[deprecated, simp, rclike_simps, norm_cast]
-theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
-  map_bit1 (algebraMap ℝ K) r
-#align is_R_or_C.of_real_bit1 RCLike.ofReal_bit1
+-- replaced by `RCLike.ofReal_ofNat`
+#noalign is_R_or_C.of_real_bit0
+#noalign is_R_or_C.of_real_bit1
 
 @[simp, norm_cast, rclike_simps]
 theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : K) = -r :=
@@ -368,17 +344,15 @@ theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) := by
   simp only [ofReal_im, conj_im, eq_self_iff_true, conj_re, and_self_iff, neg_zero]
 #align is_R_or_C.conj_of_real RCLike.conj_ofReal
 
-set_option linter.deprecated false in
-@[deprecated, rclike_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
-theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
-  map_bit0 _ _
-#align is_R_or_C.conj_bit0 RCLike.conj_bit0
-
-set_option linter.deprecated false in
-@[deprecated, rclike_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
-theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
-  map_bit1 _ _
-#align is_R_or_C.conj_bit1 RCLike.conj_bit1
+-- replaced by `RCLike.conj_ofNat`
+#noalign is_R_or_C.conj_bit0
+#noalign is_R_or_C.conj_bit1
+
+theorem conj_nat_cast (n : ℕ) : conj (n : K) = n := map_natCast _ _
+
+-- See note [no_index around OfNat.ofNat]
+theorem conj_ofNat (n : ℕ) [n.AtLeastTwo] : conj (no_index (OfNat.ofNat n : K)) = OfNat.ofNat n :=
+  map_ofNat _ _
 
 @[rclike_simps] -- Porting note (#10618): was a `simp` but `simp` can prove it
 theorem conj_neg_I : conj (-I) = (I : K) := by rw [map_neg, conj_I, neg_neg]

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.

@@ -11,9 +11,9 @@ import Mathlib.Analysis.NormedSpace.Basic
 #align_import data.is_R_or_C.basic from "leanprover-community/mathlib"@"baa88307f3e699fa7054ef04ec79fa4f056169cb"
 
 /-!
-# `IsROrC`: a typeclass for ℝ or ℂ
+# `RCLike`: a typeclass for ℝ or ℂ
 
-This file defines the typeclass `IsROrC` intended to have only two instances:
+This file defines the typeclass `RCLike` intended to have only two instances:
 ℝ and ℂ. It is meant for definitions and theorems which hold for both the real and the complex case,
 and in particular when the real case follows directly from the complex case by setting `re` to `id`,
 `im` to zero and so on. Its API follows closely that of ℂ.
@@ -28,7 +28,7 @@ The instance for `ℂ` is declared in `Mathlib/Analysis/Complex/Basic.lean`.
 
 ## Implementation notes
 
-The coercion from reals into an `IsROrC` field is done by registering `IsROrC.ofReal` as
+The coercion from reals into an `RCLike` field is done by registering `RCLike.ofReal` as
 a `CoeTC`. For this to work, we must proceed carefully to avoid problems involving circular
 coercions in the case `K=ℝ`; in particular, we cannot use the plain `Coe` and must set
 priorities carefully. This problem was already solved for `ℕ`, and we copy the solution detailed
@@ -37,7 +37,7 @@ in `Mathlib/Data/Nat/Cast/Defs.lean`. See also Note [coercion into rings] for mo
 In addition, several lemmas need to be set at priority 900 to make sure that they do not override
 their counterparts in `Mathlib/Analysis/Complex/Basic.lean` (which causes linter errors).
 
-A few lemmas requiring heavier imports are in `Mathlib/Data/IsROrC/Lemmas.lean`.
+A few lemmas requiring heavier imports are in `Mathlib/Data/RCLike/Lemmas.lean`.
 -/
 
 set_option autoImplicit true
@@ -54,7 +54,7 @@ open ComplexConjugate
 /--
 This typeclass captures properties shared by ℝ and ℂ, with an API that closely matches that of ℂ.
 -/
-class IsROrC (K : semiOutParam (Type*)) extends DenselyNormedField K, StarRing K,
+class RCLike (K : semiOutParam (Type*)) extends DenselyNormedField K, StarRing K,
     NormedAlgebra ℝ K, CompleteSpace K where
   re : K →+ ℝ
   im : K →+ ℝ
@@ -77,345 +77,345 @@ class IsROrC (K : semiOutParam (Type*)) extends DenselyNormedField K, StarRing K
   le_iff_re_im : z ≤ w ↔ re z ≤ re w ∧ im z = im w
   -- note we cannot put this in the `extends` clause
   [toDecidableEq : DecidableEq K]
-#align is_R_or_C IsROrC
+#align is_R_or_C RCLike
 
-scoped[ComplexOrder] attribute [instance 100] IsROrC.toPartialOrder
-attribute [instance 100] IsROrC.toDecidableEq
+scoped[ComplexOrder] attribute [instance 100] RCLike.toPartialOrder
+attribute [instance 100] RCLike.toDecidableEq
 
 end
 
-variable {K E : Type*} [IsROrC K]
+variable {K E : Type*} [RCLike K]
 
-namespace IsROrC
+namespace RCLike
 
 open ComplexConjugate
 
-/-- Coercion from `ℝ` to an `IsROrC` field. -/
+/-- Coercion from `ℝ` to an `RCLike` field. -/
 @[coe] abbrev ofReal : ℝ → K := Algebra.cast
 
 /- The priority must be set at 900 to ensure that coercions are tried in the right order.
 See Note [coercion into rings], or `Mathlib/Data/Nat/Cast/Basic.lean` for more details. -/
 noncomputable instance (priority := 900) algebraMapCoe : CoeTC ℝ K :=
   ⟨ofReal⟩
-#align is_R_or_C.algebra_map_coe IsROrC.algebraMapCoe
+#align is_R_or_C.algebra_map_coe RCLike.algebraMapCoe
 
 theorem ofReal_alg (x : ℝ) : (x : K) = x • (1 : K) :=
   Algebra.algebraMap_eq_smul_one x
-#align is_R_or_C.of_real_alg IsROrC.ofReal_alg
+#align is_R_or_C.of_real_alg RCLike.ofReal_alg
 
 theorem real_smul_eq_coe_mul (r : ℝ) (z : K) : r • z = (r : K) * z :=
   Algebra.smul_def r z
-#align is_R_or_C.real_smul_eq_coe_mul IsROrC.real_smul_eq_coe_mul
+#align is_R_or_C.real_smul_eq_coe_mul RCLike.real_smul_eq_coe_mul
 
 theorem real_smul_eq_coe_smul [AddCommGroup E] [Module K E] [Module ℝ E] [IsScalarTower ℝ K E]
-    (r : ℝ) (x : E) : r • x = (r : K) • x := by rw [IsROrC.ofReal_alg, smul_one_smul]
-#align is_R_or_C.real_smul_eq_coe_smul IsROrC.real_smul_eq_coe_smul
+    (r : ℝ) (x : E) : r • x = (r : K) • x := by rw [RCLike.ofReal_alg, smul_one_smul]
+#align is_R_or_C.real_smul_eq_coe_smul RCLike.real_smul_eq_coe_smul
 
 theorem algebraMap_eq_ofReal : ⇑(algebraMap ℝ K) = ofReal :=
   rfl
-#align is_R_or_C.algebra_map_eq_of_real IsROrC.algebraMap_eq_ofReal
+#align is_R_or_C.algebra_map_eq_of_real RCLike.algebraMap_eq_ofReal
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem re_add_im (z : K) : (re z : K) + im z * I = z :=
-  IsROrC.re_add_im_ax z
-#align is_R_or_C.re_add_im IsROrC.re_add_im
+  RCLike.re_add_im_ax z
+#align is_R_or_C.re_add_im RCLike.re_add_im
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_re : ∀ r : ℝ, re (r : K) = r :=
-  IsROrC.ofReal_re_ax
-#align is_R_or_C.of_real_re IsROrC.ofReal_re
+  RCLike.ofReal_re_ax
+#align is_R_or_C.of_real_re RCLike.ofReal_re
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_im : ∀ r : ℝ, im (r : K) = 0 :=
-  IsROrC.ofReal_im_ax
-#align is_R_or_C.of_real_im IsROrC.ofReal_im
+  RCLike.ofReal_im_ax
+#align is_R_or_C.of_real_im RCLike.ofReal_im
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem mul_re : ∀ z w : K, re (z * w) = re z * re w - im z * im w :=
-  IsROrC.mul_re_ax
-#align is_R_or_C.mul_re IsROrC.mul_re
+  RCLike.mul_re_ax
+#align is_R_or_C.mul_re RCLike.mul_re
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem mul_im : ∀ z w : K, im (z * w) = re z * im w + im z * re w :=
-  IsROrC.mul_im_ax
-#align is_R_or_C.mul_im IsROrC.mul_im
+  RCLike.mul_im_ax
+#align is_R_or_C.mul_im RCLike.mul_im
 
 theorem ext_iff {z w : K} : z = w ↔ re z = re w ∧ im z = im w :=
   ⟨fun h => h ▸ ⟨rfl, rfl⟩, fun ⟨h₁, h₂⟩ => re_add_im z ▸ re_add_im w ▸ h₁ ▸ h₂ ▸ rfl⟩
-#align is_R_or_C.ext_iff IsROrC.ext_iff
+#align is_R_or_C.ext_iff RCLike.ext_iff
 
 theorem ext {z w : K} (hre : re z = re w) (him : im z = im w) : z = w :=
   ext_iff.2 ⟨hre, him⟩
-#align is_R_or_C.ext IsROrC.ext
+#align is_R_or_C.ext RCLike.ext
 
 @[norm_cast]
 theorem ofReal_zero : ((0 : ℝ) : K) = 0 :=
   algebraMap.coe_zero
-#align is_R_or_C.of_real_zero IsROrC.ofReal_zero
+#align is_R_or_C.of_real_zero RCLike.ofReal_zero
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem zero_re' : re (0 : K) = (0 : ℝ) :=
   map_zero re
-#align is_R_or_C.zero_re' IsROrC.zero_re'
+#align is_R_or_C.zero_re' RCLike.zero_re'
 
 @[norm_cast]
 theorem ofReal_one : ((1 : ℝ) : K) = 1 :=
   map_one (algebraMap ℝ K)
-#align is_R_or_C.of_real_one IsROrC.ofReal_one
+#align is_R_or_C.of_real_one RCLike.ofReal_one
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem one_re : re (1 : K) = 1 := by rw [← ofReal_one, ofReal_re]
-#align is_R_or_C.one_re IsROrC.one_re
+#align is_R_or_C.one_re RCLike.one_re
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem one_im : im (1 : K) = 0 := by rw [← ofReal_one, ofReal_im]
-#align is_R_or_C.one_im IsROrC.one_im
+#align is_R_or_C.one_im RCLike.one_im
 
 theorem ofReal_injective : Function.Injective ((↑) : ℝ → K) :=
   (algebraMap ℝ K).injective
-#align is_R_or_C.of_real_injective IsROrC.ofReal_injective
+#align is_R_or_C.of_real_injective RCLike.ofReal_injective
 
 @[norm_cast]
 theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
   algebraMap.coe_inj
-#align is_R_or_C.of_real_inj IsROrC.ofReal_inj
+#align is_R_or_C.of_real_inj RCLike.ofReal_inj
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
+@[deprecated, rclike_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
 theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
   map_bit0 _ _
-#align is_R_or_C.bit0_re IsROrC.bit0_re
+#align is_R_or_C.bit0_re RCLike.bit0_re
 
 set_option linter.deprecated false in
-@[deprecated, simp, isROrC_simps]
+@[deprecated, simp, rclike_simps]
 theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_add, bit0_re, one_re]
-#align is_R_or_C.bit1_re IsROrC.bit1_re
+#align is_R_or_C.bit1_re RCLike.bit1_re
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
+@[deprecated, rclike_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
 theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
   map_bit0 _ _
-#align is_R_or_C.bit0_im IsROrC.bit0_im
+#align is_R_or_C.bit0_im RCLike.bit0_im
 
 set_option linter.deprecated false in
-@[deprecated, simp, isROrC_simps]
+@[deprecated, simp, rclike_simps]
 theorem bit1_im (z : K) : im (bit1 z) = bit0 (im z) := by
   simp only [bit1, map_add, bit0_im, one_im, add_zero]
-#align is_R_or_C.bit1_im IsROrC.bit1_im
+#align is_R_or_C.bit1_im RCLike.bit1_im
 
 theorem ofReal_eq_zero {x : ℝ} : (x : K) = 0 ↔ x = 0 :=
   algebraMap.lift_map_eq_zero_iff x
-#align is_R_or_C.of_real_eq_zero IsROrC.ofReal_eq_zero
+#align is_R_or_C.of_real_eq_zero RCLike.ofReal_eq_zero
 
 theorem ofReal_ne_zero {x : ℝ} : (x : K) ≠ 0 ↔ x ≠ 0 :=
   ofReal_eq_zero.not
-#align is_R_or_C.of_real_ne_zero IsROrC.ofReal_ne_zero
+#align is_R_or_C.of_real_ne_zero RCLike.ofReal_ne_zero
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : K) = r + s :=
   algebraMap.coe_add _ _
-#align is_R_or_C.of_real_add IsROrC.ofReal_add
+#align is_R_or_C.of_real_add RCLike.ofReal_add
 
 set_option linter.deprecated false in
-@[deprecated, simp, isROrC_simps, norm_cast]
+@[deprecated, simp, rclike_simps, norm_cast]
 theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : K) = bit0 (r : K) :=
   ofReal_add _ _
-#align is_R_or_C.of_real_bit0 IsROrC.ofReal_bit0
+#align is_R_or_C.of_real_bit0 RCLike.ofReal_bit0
 
 set_option linter.deprecated false in
-@[deprecated, simp, isROrC_simps, norm_cast]
+@[deprecated, simp, rclike_simps, norm_cast]
 theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : K) = bit1 (r : K) :=
   map_bit1 (algebraMap ℝ K) r
-#align is_R_or_C.of_real_bit1 IsROrC.ofReal_bit1
+#align is_R_or_C.of_real_bit1 RCLike.ofReal_bit1
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : K) = -r :=
   algebraMap.coe_neg r
-#align is_R_or_C.of_real_neg IsROrC.ofReal_neg
+#align is_R_or_C.of_real_neg RCLike.ofReal_neg
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
   map_sub (algebraMap ℝ K) r s
-#align is_R_or_C.of_real_sub IsROrC.ofReal_sub
+#align is_R_or_C.of_real_sub RCLike.ofReal_sub
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_sum {α : Type*} (s : Finset α) (f : α → ℝ) :
     ((∑ i in s, f i : ℝ) : K) = ∑ i in s, (f i : K) :=
   map_sum (algebraMap ℝ K) _ _
-#align is_R_or_C.of_real_sum IsROrC.ofReal_sum
+#align is_R_or_C.of_real_sum RCLike.ofReal_sum
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_finsupp_sum {α M : Type*} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.sum fun a b => g a b : ℝ) : K) = f.sum fun a b => (g a b : K) :=
   map_finsupp_sum (algebraMap ℝ K) f g
-#align is_R_or_C.of_real_finsupp_sum IsROrC.ofReal_finsupp_sum
+#align is_R_or_C.of_real_finsupp_sum RCLike.ofReal_finsupp_sum
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : K) = r * s :=
   algebraMap.coe_mul _ _
-#align is_R_or_C.of_real_mul IsROrC.ofReal_mul
+#align is_R_or_C.of_real_mul RCLike.ofReal_mul
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = (r : K) ^ n :=
   map_pow (algebraMap ℝ K) r n
-#align is_R_or_C.of_real_pow IsROrC.ofReal_pow
+#align is_R_or_C.of_real_pow RCLike.ofReal_pow
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_prod {α : Type*} (s : Finset α) (f : α → ℝ) :
     ((∏ i in s, f i : ℝ) : K) = ∏ i in s, (f i : K) :=
   map_prod (algebraMap ℝ K) _ _
-#align is_R_or_C.of_real_prod IsROrC.ofReal_prod
+#align is_R_or_C.of_real_prod RCLike.ofReal_prod
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_finsupp_prod {α M : Type*} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.prod fun a b => g a b : ℝ) : K) = f.prod fun a b => (g a b : K) :=
   map_finsupp_prod _ f g
-#align is_R_or_C.of_real_finsupp_prod IsROrC.ofReal_finsupp_prod
+#align is_R_or_C.of_real_finsupp_prod RCLike.ofReal_finsupp_prod
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem real_smul_ofReal (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
   real_smul_eq_coe_mul _ _
-#align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofReal
+#align is_R_or_C.real_smul_of_real RCLike.real_smul_ofReal
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem re_ofReal_mul (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
   simp only [mul_re, ofReal_im, zero_mul, ofReal_re, sub_zero]
-#align is_R_or_C.of_real_mul_re IsROrC.re_ofReal_mul
+#align is_R_or_C.of_real_mul_re RCLike.re_ofReal_mul
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem im_ofReal_mul (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
   simp only [add_zero, ofReal_im, zero_mul, ofReal_re, mul_im]
-#align is_R_or_C.of_real_mul_im IsROrC.im_ofReal_mul
+#align is_R_or_C.of_real_mul_im RCLike.im_ofReal_mul
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
   rw [real_smul_eq_coe_mul, re_ofReal_mul]
-#align is_R_or_C.smul_re IsROrC.smul_re
+#align is_R_or_C.smul_re RCLike.smul_re
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem smul_im (r : ℝ) (z : K) : im (r • z) = r * im z := by
   rw [real_smul_eq_coe_mul, im_ofReal_mul]
-#align is_R_or_C.smul_im IsROrC.smul_im
+#align is_R_or_C.smul_im RCLike.smul_im
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem norm_ofReal (r : ℝ) : ‖(r : K)‖ = |r| :=
   norm_algebraMap' K r
-#align is_R_or_C.norm_of_real IsROrC.norm_ofReal
+#align is_R_or_C.norm_of_real RCLike.norm_ofReal
 
 /-! ### Characteristic zero -/
 
 -- see Note [lower instance priority]
 /-- ℝ and ℂ are both of characteristic zero.  -/
-instance (priority := 100) charZero_isROrC : CharZero K :=
+instance (priority := 100) charZero_rclike : CharZero K :=
   (RingHom.charZero_iff (algebraMap ℝ K).injective).1 inferInstance
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.char_zero_R_or_C IsROrC.charZero_isROrC
+#align is_R_or_C.char_zero_R_or_C RCLike.charZero_rclike
 
 /-! ### The imaginary unit, `I` -/
 
 /-- The imaginary unit. -/
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem I_re : re (I : K) = 0 :=
   I_re_ax
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.I_re IsROrC.I_re
+#align is_R_or_C.I_re RCLike.I_re
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem I_im (z : K) : im z * im (I : K) = im z :=
   mul_im_I_ax z
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.I_im IsROrC.I_im
+#align is_R_or_C.I_im RCLike.I_im
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem I_im' (z : K) : im (I : K) * im z = im z := by rw [mul_comm, I_im]
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.I_im' IsROrC.I_im'
+#align is_R_or_C.I_im' RCLike.I_im'
 
-@[isROrC_simps] -- porting note (#10618): was `simp`
+@[rclike_simps] -- porting note (#10618): was `simp`
 theorem I_mul_re (z : K) : re (I * z) = -im z := by
   simp only [I_re, zero_sub, I_im', zero_mul, mul_re]
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.I_mul_re IsROrC.I_mul_re
+#align is_R_or_C.I_mul_re RCLike.I_mul_re
 
 theorem I_mul_I : (I : K) = 0 ∨ (I : K) * I = -1 :=
   I_mul_I_ax
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.I_mul_I IsROrC.I_mul_I
+#align is_R_or_C.I_mul_I RCLike.I_mul_I
 
 variable (𝕜) in
 lemma I_eq_zero_or_im_I_eq_one : (I : K) = 0 ∨ im (I : K) = 1 :=
   I_mul_I (K := K) |>.imp_right fun h ↦ by simpa [h] using (I_mul_re (I : K)).symm
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem conj_re (z : K) : re (conj z) = re z :=
-  IsROrC.conj_re_ax z
-#align is_R_or_C.conj_re IsROrC.conj_re
+  RCLike.conj_re_ax z
+#align is_R_or_C.conj_re RCLike.conj_re
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem conj_im (z : K) : im (conj z) = -im z :=
-  IsROrC.conj_im_ax z
-#align is_R_or_C.conj_im IsROrC.conj_im
+  RCLike.conj_im_ax z
+#align is_R_or_C.conj_im RCLike.conj_im
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem conj_I : conj (I : K) = -I :=
-  IsROrC.conj_I_ax
+  RCLike.conj_I_ax
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.conj_I IsROrC.conj_I
+#align is_R_or_C.conj_I RCLike.conj_I
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) := by
   rw [ext_iff]
   simp only [ofReal_im, conj_im, eq_self_iff_true, conj_re, and_self_iff, neg_zero]
-#align is_R_or_C.conj_of_real IsROrC.conj_ofReal
+#align is_R_or_C.conj_of_real RCLike.conj_ofReal
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
+@[deprecated, rclike_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
   map_bit0 _ _
-#align is_R_or_C.conj_bit0 IsROrC.conj_bit0
+#align is_R_or_C.conj_bit0 RCLike.conj_bit0
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
+@[deprecated, rclike_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
   map_bit1 _ _
-#align is_R_or_C.conj_bit1 IsROrC.conj_bit1
+#align is_R_or_C.conj_bit1 RCLike.conj_bit1
 
-@[isROrC_simps] -- Porting note (#10618): was a `simp` but `simp` can prove it
+@[rclike_simps] -- Porting note (#10618): was a `simp` but `simp` can prove it
 theorem conj_neg_I : conj (-I) = (I : K) := by rw [map_neg, conj_I, neg_neg]
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.conj_neg_I IsROrC.conj_neg_I
+#align is_R_or_C.conj_neg_I RCLike.conj_neg_I
 
 theorem conj_eq_re_sub_im (z : K) : conj z = re z - im z * I :=
   (congr_arg conj (re_add_im z).symm).trans <| by
     rw [map_add, map_mul, conj_I, conj_ofReal, conj_ofReal, mul_neg, sub_eq_add_neg]
-#align is_R_or_C.conj_eq_re_sub_im IsROrC.conj_eq_re_sub_im
+#align is_R_or_C.conj_eq_re_sub_im RCLike.conj_eq_re_sub_im
 
 theorem sub_conj (z : K) : z - conj z = 2 * im z * I :=
   calc
     z - conj z = re z + im z * I - (re z - im z * I) := by rw [re_add_im, ← conj_eq_re_sub_im]
     _ = 2 * im z * I := by rw [add_sub_sub_cancel, ← two_mul, mul_assoc]
-#align is_R_or_C.sub_conj IsROrC.sub_conj
+#align is_R_or_C.sub_conj RCLike.sub_conj
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem conj_smul (r : ℝ) (z : K) : conj (r • z) = r • conj z := by
   rw [conj_eq_re_sub_im, conj_eq_re_sub_im, smul_re, smul_im, ofReal_mul, ofReal_mul,
     real_smul_eq_coe_mul r (_ - _), mul_sub, mul_assoc]
-#align is_R_or_C.conj_smul IsROrC.conj_smul
+#align is_R_or_C.conj_smul RCLike.conj_smul
 
 theorem add_conj (z : K) : z + conj z = 2 * re z :=
   calc
     z + conj z = re z + im z * I + (re z - im z * I) := by rw [re_add_im, conj_eq_re_sub_im]
     _ = 2 * re z := by rw [add_add_sub_cancel, two_mul]
-#align is_R_or_C.add_conj IsROrC.add_conj
+#align is_R_or_C.add_conj RCLike.add_conj
 
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
   rw [add_conj, mul_div_cancel_left₀ (re z : K) two_ne_zero]
-#align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
+#align is_R_or_C.re_eq_add_conj RCLike.re_eq_add_conj
 
 theorem im_eq_conj_sub (z : K) : ↑(im z) = I * (conj z - z) / 2 := by
   rw [← neg_inj, ← ofReal_neg, ← I_mul_re, re_eq_add_conj, map_mul, conj_I, ← neg_div, ← mul_neg,
     neg_sub, mul_sub, neg_mul, sub_eq_add_neg]
-#align is_R_or_C.im_eq_conj_sub IsROrC.im_eq_conj_sub
+#align is_R_or_C.im_eq_conj_sub RCLike.im_eq_conj_sub
 
 open List in
 /-- There are several equivalent ways to say that a number `z` is in fact a real number. -/
@@ -430,24 +430,24 @@ theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(r
   tfae_have 3 → 2; exact fun h => ⟨_, h⟩
   tfae_have 2 → 1; exact fun ⟨r, hr⟩ => hr ▸ conj_ofReal _
   tfae_finish
-#align is_R_or_C.is_real_tfae IsROrC.is_real_TFAE
+#align is_R_or_C.is_real_tfae RCLike.is_real_TFAE
 
 theorem conj_eq_iff_real {z : K} : conj z = z ↔ ∃ r : ℝ, z = (r : K) :=
   ((is_real_TFAE z).out 0 1).trans <| by simp only [eq_comm]
-#align is_R_or_C.conj_eq_iff_real IsROrC.conj_eq_iff_real
+#align is_R_or_C.conj_eq_iff_real RCLike.conj_eq_iff_real
 
 theorem conj_eq_iff_re {z : K} : conj z = z ↔ (re z : K) = z :=
   (is_real_TFAE z).out 0 2
-#align is_R_or_C.conj_eq_iff_re IsROrC.conj_eq_iff_re
+#align is_R_or_C.conj_eq_iff_re RCLike.conj_eq_iff_re
 
 theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
   (is_real_TFAE z).out 0 3
-#align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_im
+#align is_R_or_C.conj_eq_iff_im RCLike.conj_eq_iff_im
 
 @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
   rfl
-#align is_R_or_C.star_def IsROrC.star_def
+#align is_R_or_C.star_def RCLike.star_def
 
 variable (K)
 
@@ -455,7 +455,7 @@ variable (K)
 sesquilinear product. -/
 abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
   starRingEquiv
-#align is_R_or_C.conj_to_ring_equiv IsROrC.conjToRingEquiv
+#align is_R_or_C.conj_to_ring_equiv RCLike.conjToRingEquiv
 
 variable {K} {z : K}
 
@@ -467,96 +467,96 @@ def normSq : K →*₀ ℝ where
   map_mul' z w := by
     simp only [mul_im, mul_re]
     ring
-#align is_R_or_C.norm_sq IsROrC.normSq
+#align is_R_or_C.norm_sq RCLike.normSq
 
 theorem normSq_apply (z : K) : normSq z = re z * re z + im z * im z :=
   rfl
-#align is_R_or_C.norm_sq_apply IsROrC.normSq_apply
+#align is_R_or_C.norm_sq_apply RCLike.normSq_apply
 
 theorem norm_sq_eq_def {z : K} : ‖z‖ ^ 2 = re z * re z + im z * im z :=
   norm_sq_eq_def_ax z
-#align is_R_or_C.norm_sq_eq_def IsROrC.norm_sq_eq_def
+#align is_R_or_C.norm_sq_eq_def RCLike.norm_sq_eq_def
 
 theorem normSq_eq_def' (z : K) : normSq z = ‖z‖ ^ 2 :=
   norm_sq_eq_def.symm
-#align is_R_or_C.norm_sq_eq_def' IsROrC.normSq_eq_def'
+#align is_R_or_C.norm_sq_eq_def' RCLike.normSq_eq_def'
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem normSq_zero : normSq (0 : K) = 0 :=
   normSq.map_zero
-#align is_R_or_C.norm_sq_zero IsROrC.normSq_zero
+#align is_R_or_C.norm_sq_zero RCLike.normSq_zero
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem normSq_one : normSq (1 : K) = 1 :=
   normSq.map_one
-#align is_R_or_C.norm_sq_one IsROrC.normSq_one
+#align is_R_or_C.norm_sq_one RCLike.normSq_one
 
 theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
-#align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonneg
+#align is_R_or_C.norm_sq_nonneg RCLike.normSq_nonneg
 
-@[isROrC_simps] -- porting note (#10618): was `simp`
+@[rclike_simps] -- porting note (#10618): was `simp`
 theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 :=
   map_eq_zero _
-#align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zero
+#align is_R_or_C.norm_sq_eq_zero RCLike.normSq_eq_zero
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem normSq_pos {z : K} : 0 < normSq z ↔ z ≠ 0 := by
   rw [lt_iff_le_and_ne, Ne, eq_comm]; simp [normSq_nonneg]
-#align is_R_or_C.norm_sq_pos IsROrC.normSq_pos
+#align is_R_or_C.norm_sq_pos RCLike.normSq_pos
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem normSq_neg (z : K) : normSq (-z) = normSq z := by simp only [normSq_eq_def', norm_neg]
-#align is_R_or_C.norm_sq_neg IsROrC.normSq_neg
+#align is_R_or_C.norm_sq_neg RCLike.normSq_neg
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
-  simp only [normSq_apply, neg_mul, mul_neg, neg_neg, isROrC_simps]
-#align is_R_or_C.norm_sq_conj IsROrC.normSq_conj
+  simp only [normSq_apply, neg_mul, mul_neg, neg_neg, rclike_simps]
+#align is_R_or_C.norm_sq_conj RCLike.normSq_conj
 
-@[isROrC_simps] -- porting note (#10618): was `simp`
+@[rclike_simps] -- porting note (#10618): was `simp`
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
   map_mul _ z w
-#align is_R_or_C.norm_sq_mul IsROrC.normSq_mul
+#align is_R_or_C.norm_sq_mul RCLike.normSq_mul
 
 theorem normSq_add (z w : K) : normSq (z + w) = normSq z + normSq w + 2 * re (z * conj w) := by
-  simp only [normSq_apply, map_add, isROrC_simps]
+  simp only [normSq_apply, map_add, rclike_simps]
   ring
-#align is_R_or_C.norm_sq_add IsROrC.normSq_add
+#align is_R_or_C.norm_sq_add RCLike.normSq_add
 
 theorem re_sq_le_normSq (z : K) : re z * re z ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
-#align is_R_or_C.re_sq_le_norm_sq IsROrC.re_sq_le_normSq
+#align is_R_or_C.re_sq_le_norm_sq RCLike.re_sq_le_normSq
 
 theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
-#align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
+#align is_R_or_C.im_sq_le_norm_sq RCLike.im_sq_le_normSq
 
 theorem mul_conj (z : K) : z * conj z = ‖z‖ ^ 2 := by
   apply ext <;> simp [← ofReal_pow, norm_sq_eq_def, mul_comm]
 
-#align is_R_or_C.mul_conj IsROrC.mul_conj
+#align is_R_or_C.mul_conj RCLike.mul_conj
 
 theorem conj_mul (z : K) : conj z * z = ‖z‖ ^ 2 := by rw [mul_comm, mul_conj]
-#align is_R_or_C.conj_mul IsROrC.conj_mul
+#align is_R_or_C.conj_mul RCLike.conj_mul
 
 lemma inv_eq_conj (hz : ‖z‖ = 1) : z⁻¹ = conj z :=
   inv_eq_of_mul_eq_one_left $ by simp_rw [conj_mul, hz, algebraMap.coe_one, one_pow]
 
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [normSq_add, sub_eq_add_neg, map_neg, mul_neg, normSq_neg, map_neg]
-#align is_R_or_C.norm_sq_sub IsROrC.normSq_sub
+#align is_R_or_C.norm_sq_sub RCLike.normSq_sub
 
 theorem sqrt_normSq_eq_norm {z : K} : Real.sqrt (normSq z) = ‖z‖ := by
   rw [normSq_eq_def', Real.sqrt_sq (norm_nonneg _)]
-#align is_R_or_C.sqrt_norm_sq_eq_norm IsROrC.sqrt_normSq_eq_norm
+#align is_R_or_C.sqrt_norm_sq_eq_norm RCLike.sqrt_normSq_eq_norm
 
 /-! ### Inversion -/
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : K) = (r : K)⁻¹ :=
   map_inv₀ _ r
-#align is_R_or_C.of_real_inv IsROrC.ofReal_inv
+#align is_R_or_C.of_real_inv RCLike.ofReal_inv
 
 theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) := by
   rcases eq_or_ne z 0 with (rfl | h₀)
@@ -564,32 +564,32 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) := by
   · apply inv_eq_of_mul_eq_one_right
     rw [← mul_assoc, mul_conj, ofReal_inv, ofReal_pow, mul_inv_cancel]
     simpa
-#align is_R_or_C.inv_def IsROrC.inv_def
+#align is_R_or_C.inv_def RCLike.inv_def
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
   rw [inv_def, normSq_eq_def', mul_comm, re_ofReal_mul, conj_re, div_eq_inv_mul]
-#align is_R_or_C.inv_re IsROrC.inv_re
+#align is_R_or_C.inv_re RCLike.inv_re
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
   rw [inv_def, normSq_eq_def', mul_comm, im_ofReal_mul, conj_im, div_eq_inv_mul]
-#align is_R_or_C.inv_im IsROrC.inv_im
+#align is_R_or_C.inv_im RCLike.inv_im
 
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, neg_mul, mul_neg, neg_neg, map_neg,
-    isROrC_simps]
-#align is_R_or_C.div_re IsROrC.div_re
+    rclike_simps]
+#align is_R_or_C.div_re RCLike.div_re
 
 theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / normSq w := by
   simp only [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm, neg_mul, mul_neg, map_neg,
-    isROrC_simps]
-#align is_R_or_C.div_im IsROrC.div_im
+    rclike_simps]
+#align is_R_or_C.div_im RCLike.div_im
 
-@[isROrC_simps] -- porting note (#10618): was `simp`
+@[rclike_simps] -- porting note (#10618): was `simp`
 theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
-#align is_R_or_C.conj_inv IsROrC.conj_inv
+#align is_R_or_C.conj_inv RCLike.conj_inv
 
 lemma conj_div (x y : K) : conj (x / y) = conj x / conj y := map_div' conj conj_inv _ _
 
@@ -604,82 +604,82 @@ lemma exists_norm_mul_eq_self (x : K) : ∃ c, ‖c‖ = 1 ∧ c * ‖x‖ = x :
   · exact ⟨1, by simp⟩
   · exact ⟨x / ‖x‖, by simp [norm_ne_zero_iff.2, hx]⟩
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
   map_div₀ (algebraMap ℝ K) r s
-#align is_R_or_C.of_real_div IsROrC.ofReal_div
+#align is_R_or_C.of_real_div RCLike.ofReal_div
 
 theorem div_re_ofReal {z : K} {r : ℝ} : re (z / r) = re z / r := by
   rw [div_eq_inv_mul, div_eq_inv_mul, ← ofReal_inv, re_ofReal_mul]
-#align is_R_or_C.div_re_of_real IsROrC.div_re_ofReal
+#align is_R_or_C.div_re_of_real RCLike.div_re_ofReal
 
-@[simp, norm_cast, isROrC_simps]
+@[simp, norm_cast, rclike_simps]
 theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : K) = (r : K) ^ n :=
   map_zpow₀ (algebraMap ℝ K) r n
-#align is_R_or_C.of_real_zpow IsROrC.ofReal_zpow
+#align is_R_or_C.of_real_zpow RCLike.ofReal_zpow
 
 theorem I_mul_I_of_nonzero : (I : K) ≠ 0 → (I : K) * I = -1 :=
   I_mul_I_ax.resolve_left
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.I_mul_I_of_nonzero IsROrC.I_mul_I_of_nonzero
+#align is_R_or_C.I_mul_I_of_nonzero RCLike.I_mul_I_of_nonzero
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem inv_I : (I : K)⁻¹ = -I := by
   by_cases h : (I : K) = 0
   · simp [h]
   · field_simp [I_mul_I_of_nonzero h]
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.inv_I IsROrC.inv_I
+#align is_R_or_C.inv_I RCLike.inv_I
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem div_I (z : K) : z / I = -(z * I) := by rw [div_eq_mul_inv, inv_I, mul_neg]
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.div_I IsROrC.div_I
+#align is_R_or_C.div_I RCLike.div_I
 
-@[isROrC_simps] -- porting note (#10618): was `simp`
+@[rclike_simps] -- porting note (#10618): was `simp`
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ normSq z
-#align is_R_or_C.norm_sq_inv IsROrC.normSq_inv
+#align is_R_or_C.norm_sq_inv RCLike.normSq_inv
 
-@[isROrC_simps] -- porting note (#10618): was `simp`
+@[rclike_simps] -- porting note (#10618): was `simp`
 theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w
-#align is_R_or_C.norm_sq_div IsROrC.normSq_div
+#align is_R_or_C.norm_sq_div RCLike.normSq_div
 
-@[isROrC_simps] -- porting note (#10618): was `simp`
+@[rclike_simps] -- porting note (#10618): was `simp`
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_normSq_eq_norm, normSq_conj]
-#align is_R_or_C.norm_conj IsROrC.norm_conj
+#align is_R_or_C.norm_conj RCLike.norm_conj
 
 instance (priority := 100) : CstarRing K where
   norm_star_mul_self {x} := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) norm_conj
 
 /-! ### Cast lemmas -/
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_natCast (n : ℕ) : ((n : ℝ) : K) = n :=
   map_natCast (algebraMap ℝ K) n
-#align is_R_or_C.of_real_nat_cast IsROrC.ofReal_natCast
+#align is_R_or_C.of_real_nat_cast RCLike.ofReal_natCast
 
-@[simp, isROrC_simps] -- Porting note: removed `norm_cast`
+@[simp, rclike_simps] -- Porting note: removed `norm_cast`
 theorem natCast_re (n : ℕ) : re (n : K) = n := by rw [← ofReal_natCast, ofReal_re]
-#align is_R_or_C.nat_cast_re IsROrC.natCast_re
+#align is_R_or_C.nat_cast_re RCLike.natCast_re
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem natCast_im (n : ℕ) : im (n : K) = 0 := by rw [← ofReal_natCast, ofReal_im]
-#align is_R_or_C.nat_cast_im IsROrC.natCast_im
+#align is_R_or_C.nat_cast_im RCLike.natCast_im
 
 -- See note [no_index around OfNat.ofNat]
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem ofNat_re (n : ℕ) [n.AtLeastTwo] : re (no_index (OfNat.ofNat n) : K) = OfNat.ofNat n :=
   natCast_re n
 
 -- See note [no_index around OfNat.ofNat]
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem ofNat_im (n : ℕ) [n.AtLeastTwo] : im (no_index (OfNat.ofNat n) : K) = 0 :=
   natCast_im n
 
 -- See note [no_index around OfNat.ofNat]
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
     ((no_index (OfNat.ofNat n) : ℝ) : K) = OfNat.ofNat n :=
   ofReal_natCast n
@@ -692,158 +692,158 @@ theorem ofNat_mul_im (n : ℕ) [n.AtLeastTwo] (z : K) :
     im (OfNat.ofNat n * z) = OfNat.ofNat n * im z := by
   rw [← ofReal_ofNat, im_ofReal_mul]
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : K) = n :=
   map_intCast _ n
-#align is_R_or_C.of_real_int_cast IsROrC.ofReal_intCast
+#align is_R_or_C.of_real_int_cast RCLike.ofReal_intCast
 
-@[simp, isROrC_simps] -- Porting note: removed `norm_cast`
+@[simp, rclike_simps] -- Porting note: removed `norm_cast`
 theorem intCast_re (n : ℤ) : re (n : K) = n := by rw [← ofReal_intCast, ofReal_re]
-#align is_R_or_C.int_cast_re IsROrC.intCast_re
+#align is_R_or_C.int_cast_re RCLike.intCast_re
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem intCast_im (n : ℤ) : im (n : K) = 0 := by rw [← ofReal_intCast, ofReal_im]
-#align is_R_or_C.int_cast_im IsROrC.intCast_im
+#align is_R_or_C.int_cast_im RCLike.intCast_im
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ofReal_ratCast (n : ℚ) : ((n : ℝ) : K) = n :=
   map_ratCast _ n
-#align is_R_or_C.of_real_rat_cast IsROrC.ofReal_ratCast
+#align is_R_or_C.of_real_rat_cast RCLike.ofReal_ratCast
 
-@[simp, isROrC_simps] -- Porting note: removed `norm_cast`
+@[simp, rclike_simps] -- Porting note: removed `norm_cast`
 theorem ratCast_re (q : ℚ) : re (q : K) = q := by rw [← ofReal_ratCast, ofReal_re]
-#align is_R_or_C.rat_cast_re IsROrC.ratCast_re
+#align is_R_or_C.rat_cast_re RCLike.ratCast_re
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem ratCast_im (q : ℚ) : im (q : K) = 0 := by rw [← ofReal_ratCast, ofReal_im]
-#align is_R_or_C.rat_cast_im IsROrC.ratCast_im
+#align is_R_or_C.rat_cast_im RCLike.ratCast_im
 
 /-! ### Norm -/
 
 theorem norm_of_nonneg {r : ℝ} (h : 0 ≤ r) : ‖(r : K)‖ = r :=
   (norm_ofReal _).trans (abs_of_nonneg h)
-#align is_R_or_C.norm_of_nonneg IsROrC.norm_of_nonneg
+#align is_R_or_C.norm_of_nonneg RCLike.norm_of_nonneg
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n := by
   rw [← ofReal_natCast]
   exact norm_of_nonneg (Nat.cast_nonneg n)
-#align is_R_or_C.norm_nat_cast IsROrC.norm_natCast
+#align is_R_or_C.norm_nat_cast RCLike.norm_natCast
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem norm_ofNat (n : ℕ) [n.AtLeastTwo] : ‖(no_index (OfNat.ofNat n) : K)‖ = OfNat.ofNat n :=
   norm_natCast n
 
 variable (K) in
 lemma norm_nsmul [NormedAddCommGroup E] [NormedSpace K E] (n : ℕ) (x : E) : ‖n • x‖ = n • ‖x‖ := by
-  rw [nsmul_eq_smul_cast K, norm_smul, IsROrC.norm_natCast, nsmul_eq_mul]
+  rw [nsmul_eq_smul_cast K, norm_smul, RCLike.norm_natCast, nsmul_eq_mul]
 
 theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [normSq_eq_def', sq]
-#align is_R_or_C.mul_self_norm IsROrC.mul_self_norm
+#align is_R_or_C.mul_self_norm RCLike.mul_self_norm
 
-attribute [isROrC_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
+attribute [rclike_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
 
--- Porting note: removed @[simp, isROrC_simps], b/c generalized to `norm_ofNat`
+-- Porting note: removed @[simp, rclike_simps], b/c generalized to `norm_ofNat`
 theorem norm_two : ‖(2 : K)‖ = 2 := norm_ofNat 2
-#align is_R_or_C.norm_two IsROrC.norm_two
+#align is_R_or_C.norm_two RCLike.norm_two
 
 theorem abs_re_le_norm (z : K) : |re z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (abs_nonneg _) (norm_nonneg _), abs_mul_abs_self, mul_self_norm]
   apply re_sq_le_normSq
-#align is_R_or_C.abs_re_le_norm IsROrC.abs_re_le_norm
+#align is_R_or_C.abs_re_le_norm RCLike.abs_re_le_norm
 
 theorem abs_im_le_norm (z : K) : |im z| ≤ ‖z‖ := by
   rw [mul_self_le_mul_self_iff (abs_nonneg _) (norm_nonneg _), abs_mul_abs_self, mul_self_norm]
   apply im_sq_le_normSq
-#align is_R_or_C.abs_im_le_norm IsROrC.abs_im_le_norm
+#align is_R_or_C.abs_im_le_norm RCLike.abs_im_le_norm
 
 theorem norm_re_le_norm (z : K) : ‖re z‖ ≤ ‖z‖ :=
   abs_re_le_norm z
-#align is_R_or_C.norm_re_le_norm IsROrC.norm_re_le_norm
+#align is_R_or_C.norm_re_le_norm RCLike.norm_re_le_norm
 
 theorem norm_im_le_norm (z : K) : ‖im z‖ ≤ ‖z‖ :=
   abs_im_le_norm z
-#align is_R_or_C.norm_im_le_norm IsROrC.norm_im_le_norm
+#align is_R_or_C.norm_im_le_norm RCLike.norm_im_le_norm
 
 theorem re_le_norm (z : K) : re z ≤ ‖z‖ :=
   (abs_le.1 (abs_re_le_norm z)).2
-#align is_R_or_C.re_le_norm IsROrC.re_le_norm
+#align is_R_or_C.re_le_norm RCLike.re_le_norm
 
 theorem im_le_norm (z : K) : im z ≤ ‖z‖ :=
   (abs_le.1 (abs_im_le_norm _)).2
-#align is_R_or_C.im_le_norm IsROrC.im_le_norm
+#align is_R_or_C.im_le_norm RCLike.im_le_norm
 
 theorem im_eq_zero_of_le {a : K} (h : ‖a‖ ≤ re a) : im a = 0 := by
   simpa only [mul_self_norm a, normSq_apply, self_eq_add_right, mul_self_eq_zero]
     using congr_arg (fun z => z * z) ((re_le_norm a).antisymm h)
-#align is_R_or_C.im_eq_zero_of_le IsROrC.im_eq_zero_of_le
+#align is_R_or_C.im_eq_zero_of_le RCLike.im_eq_zero_of_le
 
 theorem re_eq_self_of_le {a : K} (h : ‖a‖ ≤ re a) : (re a : K) = a := by
   rw [← conj_eq_iff_re, conj_eq_iff_im, im_eq_zero_of_le h]
-#align is_R_or_C.re_eq_self_of_le IsROrC.re_eq_self_of_le
+#align is_R_or_C.re_eq_self_of_le RCLike.re_eq_self_of_le
 
 open IsAbsoluteValue
 
 theorem abs_re_div_norm_le_one (z : K) : |re z / ‖z‖| ≤ 1 := by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_re_le_norm _) (norm_nonneg _)
-#align is_R_or_C.abs_re_div_norm_le_one IsROrC.abs_re_div_norm_le_one
+#align is_R_or_C.abs_re_div_norm_le_one RCLike.abs_re_div_norm_le_one
 
 theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 := by
   rw [abs_div, abs_norm]
   exact div_le_one_of_le (abs_im_le_norm _) (norm_nonneg _)
-#align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
+#align is_R_or_C.abs_im_div_norm_le_one RCLike.abs_im_div_norm_le_one
 
 theorem norm_I_of_ne_zero (hI : (I : K) ≠ 0) : ‖(I : K)‖ = 1 := by
   rw [← mul_self_inj_of_nonneg (norm_nonneg I) zero_le_one, one_mul, ← norm_mul,
     I_mul_I_of_nonzero hI, norm_neg, norm_one]
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.norm_I_of_ne_zero IsROrC.norm_I_of_ne_zero
+#align is_R_or_C.norm_I_of_ne_zero RCLike.norm_I_of_ne_zero
 
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, ← ofReal_pow]; simp [-ofReal_pow]
-#align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj
+#align is_R_or_C.re_eq_norm_of_mul_conj RCLike.re_eq_norm_of_mul_conj
 
 theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
   rw [add_conj, ← ofReal_ofNat, ← ofReal_mul, norm_ofReal, sq_abs, ofReal_re]
-#align is_R_or_C.norm_sq_re_add_conj IsROrC.norm_sq_re_add_conj
+#align is_R_or_C.norm_sq_re_add_conj RCLike.norm_sq_re_add_conj
 
 theorem norm_sq_re_conj_add (x : K) : ‖conj x + x‖ ^ 2 = re (conj x + x) ^ 2 := by
   rw [add_comm, norm_sq_re_add_conj]
-#align is_R_or_C.norm_sq_re_conj_add IsROrC.norm_sq_re_conj_add
+#align is_R_or_C.norm_sq_re_conj_add RCLike.norm_sq_re_conj_add
 
 /-! ### Cauchy sequences -/
 
 theorem isCauSeq_re (f : CauSeq K norm) : IsCauSeq abs fun n => re (f n) := fun ε ε0 =>
   (f.cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_re_le_norm (f j - f i)) (H _ ij)
-#align is_R_or_C.is_cau_seq_re IsROrC.isCauSeq_re
+#align is_R_or_C.is_cau_seq_re RCLike.isCauSeq_re
 
 theorem isCauSeq_im (f : CauSeq K norm) : IsCauSeq abs fun n => im (f n) := fun ε ε0 =>
   (f.cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa only [map_sub] using abs_im_le_norm (f j - f i)) (H _ ij)
-#align is_R_or_C.is_cau_seq_im IsROrC.isCauSeq_im
+#align is_R_or_C.is_cau_seq_im RCLike.isCauSeq_im
 
 /-- The real part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_re f⟩
-#align is_R_or_C.cau_seq_re IsROrC.cauSeqRe
+#align is_R_or_C.cau_seq_re RCLike.cauSeqRe
 
 /-- The imaginary part of a K Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq K norm) : CauSeq ℝ abs :=
   ⟨_, isCauSeq_im f⟩
-#align is_R_or_C.cau_seq_im IsROrC.cauSeqIm
+#align is_R_or_C.cau_seq_im RCLike.cauSeqIm
 
 theorem isCauSeq_norm {f : ℕ → K} (hf : IsCauSeq norm f) : IsCauSeq abs (norm ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
   ⟨i, fun j hj => lt_of_le_of_lt (abs_norm_sub_norm_le _ _) (hi j hj)⟩
-#align is_R_or_C.is_cau_seq_norm IsROrC.isCauSeq_norm
+#align is_R_or_C.is_cau_seq_norm RCLike.isCauSeq_norm
 
-end IsROrC
+end RCLike
 
 section Instances
 
-noncomputable instance Real.isROrC : IsROrC ℝ where
+noncomputable instance Real.RCLike : RCLike ℝ where
   re := AddMonoidHom.id ℝ
   im := 0
   I := 0
@@ -862,11 +862,11 @@ noncomputable instance Real.isROrC : IsROrC ℝ where
     mul_zero, AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
   mul_im_I_ax _ := by simp only [mul_zero, AddMonoidHom.zero_apply]
   le_iff_re_im := (and_iff_left rfl).symm
-#align real.is_R_or_C Real.isROrC
+#align real.is_R_or_C Real.RCLike
 
 end Instances
 
-namespace IsROrC
+namespace RCLike
 
 section Order
 
@@ -874,7 +874,7 @@ open scoped ComplexOrder
 variable {z w : K}
 
 theorem lt_iff_re_im : z < w ↔ re z < re w ∧ im z = im w := by
-  simp_rw [lt_iff_le_and_ne, @IsROrC.le_iff_re_im K]
+  simp_rw [lt_iff_le_and_ne, @RCLike.le_iff_re_im K]
   constructor
   · rintro ⟨⟨hr, hi⟩, heq⟩
     exact ⟨⟨hr, mt (fun hreq => ext hreq hi) heq⟩, hi⟩
@@ -912,7 +912,7 @@ Note this is only an instance with `open scoped ComplexOrder`. -/
 def toStarOrderedRing : StarOrderedRing K :=
   StarOrderedRing.ofNonnegIff'
     (h_add := fun {x y} hxy z => by
-      rw [IsROrC.le_iff_re_im] at *
+      rw [RCLike.le_iff_re_im] at *
       simpa [map_add, add_le_add_iff_left, add_right_inj] using hxy)
     (h_nonneg_iff := fun x => by
       rw [nonneg_iff]
@@ -920,29 +920,29 @@ def toStarOrderedRing : StarOrderedRing K :=
       rintro ⟨s, rfl⟩
       simp [mul_comm, mul_self_nonneg, add_nonneg])
 
-scoped[ComplexOrder] attribute [instance] IsROrC.toStarOrderedRing
+scoped[ComplexOrder] attribute [instance] RCLike.toStarOrderedRing
 
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℝ` and `ℂ` are strictly ordered rings.
 
 Note this is only an instance with `open scoped ComplexOrder`. -/
 def toStrictOrderedCommRing : StrictOrderedCommRing K where
-  zero_le_one := by simp [@IsROrC.le_iff_re_im K]
+  zero_le_one := by simp [@RCLike.le_iff_re_im K]
   add_le_add_left _ _ := add_le_add_left
   mul_pos z w hz hw := by
     rw [lt_iff_re_im, map_zero] at hz hw ⊢
     simp [mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1]
   mul_comm := by intros; apply ext <;> ring_nf
 
-scoped[ComplexOrder] attribute [instance] IsROrC.toStrictOrderedCommRing
+scoped[ComplexOrder] attribute [instance] RCLike.toStrictOrderedCommRing
 
 theorem toOrderedSMul : OrderedSMul ℝ K :=
   OrderedSMul.mk' fun a b r hab hr => by
     replace hab := hab.le
-    rw [IsROrC.le_iff_re_im] at hab
-    rw [IsROrC.le_iff_re_im, smul_re, smul_re, smul_im, smul_im]
+    rw [RCLike.le_iff_re_im] at hab
+    rw [RCLike.le_iff_re_im, smul_re, smul_re, smul_im, smul_im]
     exact hab.imp (fun h => mul_le_mul_of_nonneg_left h hr.le) (congr_arg _)
 
-scoped[ComplexOrder] attribute [instance] IsROrC.toOrderedSMul
+scoped[ComplexOrder] attribute [instance] RCLike.toOrderedSMul
 
 end Order
 
@@ -950,108 +950,108 @@ open ComplexConjugate
 
 section CleanupLemmas
 
-local notation "reR" => @IsROrC.re ℝ _
-local notation "imR" => @IsROrC.im ℝ _
-local notation "IR" => @IsROrC.I ℝ _
-local notation "normSqR" => @IsROrC.normSq ℝ _
+local notation "reR" => @RCLike.re ℝ _
+local notation "imR" => @RCLike.im ℝ _
+local notation "IR" => @RCLike.I ℝ _
+local notation "normSqR" => @RCLike.normSq ℝ _
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem re_to_real {x : ℝ} : reR x = x :=
   rfl
-#align is_R_or_C.re_to_real IsROrC.re_to_real
+#align is_R_or_C.re_to_real RCLike.re_to_real
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem im_to_real {x : ℝ} : imR x = 0 :=
   rfl
-#align is_R_or_C.im_to_real IsROrC.im_to_real
+#align is_R_or_C.im_to_real RCLike.im_to_real
 
-@[isROrC_simps]
+@[rclike_simps]
 theorem conj_to_real {x : ℝ} : conj x = x :=
   rfl
-#align is_R_or_C.conj_to_real IsROrC.conj_to_real
+#align is_R_or_C.conj_to_real RCLike.conj_to_real
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem I_to_real : IR = 0 :=
   rfl
 set_option linter.uppercaseLean3 false in
-#align is_R_or_C.I_to_real IsROrC.I_to_real
+#align is_R_or_C.I_to_real RCLike.I_to_real
 
-@[simp, isROrC_simps]
-theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [IsROrC.normSq]
-#align is_R_or_C.norm_sq_to_real IsROrC.normSq_to_real
+@[simp, rclike_simps]
+theorem normSq_to_real {x : ℝ} : normSq x = x * x := by simp [RCLike.normSq]
+#align is_R_or_C.norm_sq_to_real RCLike.normSq_to_real
 
 @[simp]
 theorem ofReal_real_eq_id : @ofReal ℝ _ = id :=
   rfl
-#align is_R_or_C.coe_real_eq_id IsROrC.ofReal_real_eq_id
+#align is_R_or_C.coe_real_eq_id RCLike.ofReal_real_eq_id
 
 end CleanupLemmas
 
 section LinearMaps
 
-/-- The real part in an `IsROrC` field, as a linear map. -/
+/-- The real part in an `RCLike` field, as a linear map. -/
 def reLm : K →ₗ[ℝ] ℝ :=
   { re with map_smul' := smul_re }
-#align is_R_or_C.re_lm IsROrC.reLm
+#align is_R_or_C.re_lm RCLike.reLm
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem reLm_coe : (reLm : K → ℝ) = re :=
   rfl
-#align is_R_or_C.re_lm_coe IsROrC.reLm_coe
+#align is_R_or_C.re_lm_coe RCLike.reLm_coe
 
-/-- The real part in an `IsROrC` field, as a continuous linear map. -/
+/-- The real part in an `RCLike` field, as a continuous linear map. -/
 noncomputable def reCLM : K →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by
     rw [one_mul]
     exact abs_re_le_norm x
-#align is_R_or_C.re_clm IsROrC.reCLM
+#align is_R_or_C.re_clm RCLike.reCLM
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem reCLM_coe : ((reCLM : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
   rfl
-#align is_R_or_C.re_clm_coe IsROrC.reCLM_coe
+#align is_R_or_C.re_clm_coe RCLike.reCLM_coe
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem reCLM_apply : ((reCLM : K →L[ℝ] ℝ) : K → ℝ) = re :=
   rfl
-#align is_R_or_C.re_clm_apply IsROrC.reCLM_apply
+#align is_R_or_C.re_clm_apply RCLike.reCLM_apply
 
 @[continuity]
 theorem continuous_re : Continuous (re : K → ℝ) :=
   reCLM.continuous
-#align is_R_or_C.continuous_re IsROrC.continuous_re
+#align is_R_or_C.continuous_re RCLike.continuous_re
 
-/-- The imaginary part in an `IsROrC` field, as a linear map. -/
+/-- The imaginary part in an `RCLike` field, as a linear map. -/
 def imLm : K →ₗ[ℝ] ℝ :=
   { im with map_smul' := smul_im }
-#align is_R_or_C.im_lm IsROrC.imLm
+#align is_R_or_C.im_lm RCLike.imLm
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem imLm_coe : (imLm : K → ℝ) = im :=
   rfl
-#align is_R_or_C.im_lm_coe IsROrC.imLm_coe
+#align is_R_or_C.im_lm_coe RCLike.imLm_coe
 
-/-- The imaginary part in an `IsROrC` field, as a continuous linear map. -/
+/-- The imaginary part in an `RCLike` field, as a continuous linear map. -/
 noncomputable def imCLM : K →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by
     rw [one_mul]
     exact abs_im_le_norm x
-#align is_R_or_C.im_clm IsROrC.imCLM
+#align is_R_or_C.im_clm RCLike.imCLM
 
-@[simp, isROrC_simps, norm_cast]
+@[simp, rclike_simps, norm_cast]
 theorem imCLM_coe : ((imCLM : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
   rfl
-#align is_R_or_C.im_clm_coe IsROrC.imCLM_coe
+#align is_R_or_C.im_clm_coe RCLike.imCLM_coe
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem imCLM_apply : ((imCLM : K →L[ℝ] ℝ) : K → ℝ) = im :=
   rfl
-#align is_R_or_C.im_clm_apply IsROrC.imCLM_apply
+#align is_R_or_C.im_clm_apply RCLike.imCLM_apply
 
 @[continuity]
 theorem continuous_im : Continuous (im : K → ℝ) :=
   imCLM.continuous
-#align is_R_or_C.continuous_im IsROrC.continuous_im
+#align is_R_or_C.continuous_im RCLike.continuous_im
 
 /-- Conjugate as an `ℝ`-algebra equivalence -/
 def conjAe : K ≃ₐ[ℝ] K :=
@@ -1060,37 +1060,37 @@ def conjAe : K ≃ₐ[ℝ] K :=
     left_inv := conj_conj
     right_inv := conj_conj
     commutes' := conj_ofReal }
-#align is_R_or_C.conj_ae IsROrC.conjAe
+#align is_R_or_C.conj_ae RCLike.conjAe
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem conjAe_coe : (conjAe : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_ae_coe IsROrC.conjAe_coe
+#align is_R_or_C.conj_ae_coe RCLike.conjAe_coe
 
 /-- Conjugate as a linear isometry -/
 noncomputable def conjLIE : K ≃ₗᵢ[ℝ] K :=
   ⟨conjAe.toLinearEquiv, fun _ => norm_conj⟩
-#align is_R_or_C.conj_lie IsROrC.conjLIE
+#align is_R_or_C.conj_lie RCLike.conjLIE
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem conjLIE_apply : (conjLIE : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_lie_apply IsROrC.conjLIE_apply
+#align is_R_or_C.conj_lie_apply RCLike.conjLIE_apply
 
 /-- Conjugate as a continuous linear equivalence -/
 noncomputable def conjCLE : K ≃L[ℝ] K :=
   @conjLIE K _
-#align is_R_or_C.conj_cle IsROrC.conjCLE
+#align is_R_or_C.conj_cle RCLike.conjCLE
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem conjCLE_coe : (@conjCLE K _).toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
-#align is_R_or_C.conj_cle_coe IsROrC.conjCLE_coe
+#align is_R_or_C.conj_cle_coe RCLike.conjCLE_coe
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem conjCLE_apply : (conjCLE : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_cle_apply IsROrC.conjCLE_apply
+#align is_R_or_C.conj_cle_apply RCLike.conjCLE_apply
 
 instance (priority := 100) : ContinuousStar K :=
   ⟨conjLIE.continuous⟩
@@ -1098,53 +1098,53 @@ instance (priority := 100) : ContinuousStar K :=
 @[continuity]
 theorem continuous_conj : Continuous (conj : K → K) :=
   continuous_star
-#align is_R_or_C.continuous_conj IsROrC.continuous_conj
+#align is_R_or_C.continuous_conj RCLike.continuous_conj
 
 /-- The `ℝ → K` coercion, as a linear map -/
 noncomputable def ofRealAm : ℝ →ₐ[ℝ] K :=
   Algebra.ofId ℝ K
-#align is_R_or_C.of_real_am IsROrC.ofRealAm
+#align is_R_or_C.of_real_am RCLike.ofRealAm
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem ofRealAm_coe : (ofRealAm : ℝ → K) = ofReal :=
   rfl
-#align is_R_or_C.of_real_am_coe IsROrC.ofRealAm_coe
+#align is_R_or_C.of_real_am_coe RCLike.ofRealAm_coe
 
 /-- The ℝ → K coercion, as a linear isometry -/
 noncomputable def ofRealLI : ℝ →ₗᵢ[ℝ] K where
   toLinearMap := ofRealAm.toLinearMap
   norm_map' := norm_ofReal
-#align is_R_or_C.of_real_li IsROrC.ofRealLI
+#align is_R_or_C.of_real_li RCLike.ofRealLI
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem ofRealLI_apply : (ofRealLI : ℝ → K) = ofReal :=
   rfl
-#align is_R_or_C.of_real_li_apply IsROrC.ofRealLI_apply
+#align is_R_or_C.of_real_li_apply RCLike.ofRealLI_apply
 
 /-- The `ℝ → K` coercion, as a continuous linear map -/
 noncomputable def ofRealCLM : ℝ →L[ℝ] K :=
   ofRealLI.toContinuousLinearMap
-#align is_R_or_C.of_real_clm IsROrC.ofRealCLM
+#align is_R_or_C.of_real_clm RCLike.ofRealCLM
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem ofRealCLM_coe : (@ofRealCLM K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinearMap :=
   rfl
-#align is_R_or_C.of_real_clm_coe IsROrC.ofRealCLM_coe
+#align is_R_or_C.of_real_clm_coe RCLike.ofRealCLM_coe
 
-@[simp, isROrC_simps]
+@[simp, rclike_simps]
 theorem ofRealCLM_apply : (ofRealCLM : ℝ → K) = ofReal :=
   rfl
-#align is_R_or_C.of_real_clm_apply IsROrC.ofRealCLM_apply
+#align is_R_or_C.of_real_clm_apply RCLike.ofRealCLM_apply
 
 @[continuity, fun_prop]
 theorem continuous_ofReal : Continuous (ofReal : ℝ → K) :=
   ofRealLI.continuous
-#align is_R_or_C.continuous_of_real IsROrC.continuous_ofReal
+#align is_R_or_C.continuous_of_real RCLike.continuous_ofReal
 
 @[continuity]
 theorem continuous_normSq : Continuous (normSq : K → ℝ) :=
   (continuous_re.mul continuous_re).add (continuous_im.mul continuous_im)
-#align is_R_or_C.continuous_norm_sq IsROrC.continuous_normSq
+#align is_R_or_C.continuous_norm_sq RCLike.continuous_normSq
 
 end LinearMaps
 
@@ -1159,7 +1159,7 @@ lemma im_eq_zero (h : I = (0 : K)) (z : K) : im z = 0 := by
   rw [← re_add_im z, h]
   simp
 
-/-- The natural isomorphism between `𝕜` satisfying `IsROrC 𝕜` and `ℝ` when `IsROrC.I = 0`. -/
+/-- The natural isomorphism between `𝕜` satisfying `RCLike 𝕜` and `ℝ` when `RCLike.I = 0`. -/
 @[simps]
 def realRingEquiv (h : I = (0 : K)) : K ≃+* ℝ where
   toFun := re
@@ -1169,8 +1169,8 @@ def realRingEquiv (h : I = (0 : K)) : K ≃+* ℝ where
   map_add' := map_add re
   map_mul' := by simp [im_eq_zero h]
 
-/-- The natural `ℝ`-linear isometry equivalence between `𝕜` satisfying `IsROrC 𝕜` and `ℝ` when
-`IsROrC.I = 0`. -/
+/-- The natural `ℝ`-linear isometry equivalence between `𝕜` satisfying `RCLike 𝕜` and `ℝ` when
+`RCLike.I = 0`. -/
 @[simps]
 noncomputable def realLinearIsometryEquiv (h : I = (0 : K)) : K ≃ₗᵢ[ℝ] ℝ where
   map_smul' := smul_re
@@ -1179,4 +1179,4 @@ noncomputable def realLinearIsometryEquiv (h : I = (0 : K)) : K ≃ₗᵢ[ℝ] 
 
 end CaseSpecific
 
-end IsROrC
+end RCLike

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

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

| Statement | New name | Old name | |

@@ -409,7 +409,7 @@ theorem add_conj (z : K) : z + conj z = 2 * re z :=
 #align is_R_or_C.add_conj IsROrC.add_conj
 
 theorem re_eq_add_conj (z : K) : ↑(re z) = (z + conj z) / 2 := by
-  rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]
+  rw [add_conj, mul_div_cancel_left₀ (re z : K) two_ne_zero]
 #align is_R_or_C.re_eq_add_conj IsROrC.re_eq_add_conj
 
 theorem im_eq_conj_sub (z : K) : ↑(im z) = I * (conj z - z) / 2 := by

Classifies by adding issue number #10618 to porting notes claiming "simp can prove it".

@@ -181,7 +181,7 @@ theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
 #align is_R_or_C.of_real_inj IsROrC.ofReal_inj
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- porting note (#10618): was `simp` but `simp` can prove it
+@[deprecated, isROrC_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
 theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_re IsROrC.bit0_re
@@ -192,7 +192,7 @@ theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_a
 #align is_R_or_C.bit1_re IsROrC.bit1_re
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- porting note (#10618): was `simp` but `simp` can prove it
+@[deprecated, isROrC_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
 theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_im IsROrC.bit0_im
@@ -369,18 +369,18 @@ theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) := by
 #align is_R_or_C.conj_of_real IsROrC.conj_ofReal
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- porting note (#10618): was `simp` but `simp` can prove it
+@[deprecated, isROrC_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
   map_bit0 _ _
 #align is_R_or_C.conj_bit0 IsROrC.conj_bit0
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- porting note (#10618): was `simp` but `simp` can prove it
+@[deprecated, isROrC_simps] -- Porting note (#10618): was `simp` but `simp` can prove it
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
   map_bit1 _ _
 #align is_R_or_C.conj_bit1 IsROrC.conj_bit1
 
-@[isROrC_simps] -- Porting note: was a `simp` but `simp` can prove it
+@[isROrC_simps] -- Porting note (#10618): was a `simp` but `simp` can prove it
 theorem conj_neg_I : conj (-I) = (I : K) := by rw [map_neg, conj_I, neg_neg]
 set_option linter.uppercaseLean3 false in
 #align is_R_or_C.conj_neg_I IsROrC.conj_neg_I

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -380,7 +380,7 @@ theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
   map_bit1 _ _
 #align is_R_or_C.conj_bit1 IsROrC.conj_bit1
 
-@[isROrC_simps] -- porting note: was a `simp` but `simp` can prove it
+@[isROrC_simps] -- Porting note: was a `simp` but `simp` can prove it
 theorem conj_neg_I : conj (-I) = (I : K) := by rw [map_neg, conj_I, neg_neg]
 set_option linter.uppercaseLean3 false in
 #align is_R_or_C.conj_neg_I IsROrC.conj_neg_I
@@ -660,7 +660,7 @@ theorem ofReal_natCast (n : ℕ) : ((n : ℝ) : K) = n :=
   map_natCast (algebraMap ℝ K) n
 #align is_R_or_C.of_real_nat_cast IsROrC.ofReal_natCast
 
-@[simp, isROrC_simps] -- porting note: removed `norm_cast`
+@[simp, isROrC_simps] -- Porting note: removed `norm_cast`
 theorem natCast_re (n : ℕ) : re (n : K) = n := by rw [← ofReal_natCast, ofReal_re]
 #align is_R_or_C.nat_cast_re IsROrC.natCast_re
 
@@ -697,7 +697,7 @@ theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : K) = n :=
   map_intCast _ n
 #align is_R_or_C.of_real_int_cast IsROrC.ofReal_intCast
 
-@[simp, isROrC_simps] -- porting note: removed `norm_cast`
+@[simp, isROrC_simps] -- Porting note: removed `norm_cast`
 theorem intCast_re (n : ℤ) : re (n : K) = n := by rw [← ofReal_intCast, ofReal_re]
 #align is_R_or_C.int_cast_re IsROrC.intCast_re
 
@@ -710,7 +710,7 @@ theorem ofReal_ratCast (n : ℚ) : ((n : ℝ) : K) = n :=
   map_ratCast _ n
 #align is_R_or_C.of_real_rat_cast IsROrC.ofReal_ratCast
 
-@[simp, isROrC_simps] -- porting note: removed `norm_cast`
+@[simp, isROrC_simps] -- Porting note: removed `norm_cast`
 theorem ratCast_re (q : ℚ) : re (q : K) = q := by rw [← ofReal_ratCast, ofReal_re]
 #align is_R_or_C.rat_cast_re IsROrC.ratCast_re
 
@@ -743,7 +743,7 @@ theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [normSq_eq
 
 attribute [isROrC_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
 
--- porting note: removed @[simp, isROrC_simps], b/c generalized to `norm_ofNat`
+-- Porting note: removed @[simp, isROrC_simps], b/c generalized to `norm_ofNat`
 theorem norm_two : ‖(2 : K)‖ = 2 := norm_ofNat 2
 #align is_R_or_C.norm_two IsROrC.norm_two
 

Classifies by adding issue number (#10745) to porting notes claiming was simp.

@@ -181,7 +181,7 @@ theorem ofReal_inj {z w : ℝ} : (z : K) = (w : K) ↔ z = w :=
 #align is_R_or_C.of_real_inj IsROrC.ofReal_inj
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- porting note: was `simp` but `simp` can prove it
+@[deprecated, isROrC_simps] -- porting note (#10618): was `simp` but `simp` can prove it
 theorem bit0_re (z : K) : re (bit0 z) = bit0 (re z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_re IsROrC.bit0_re
@@ -192,7 +192,7 @@ theorem bit1_re (z : K) : re (bit1 z) = bit1 (re z) := by simp only [bit1, map_a
 #align is_R_or_C.bit1_re IsROrC.bit1_re
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- porting note: was `simp` but `simp` can prove it
+@[deprecated, isROrC_simps] -- porting note (#10618): was `simp` but `simp` can prove it
 theorem bit0_im (z : K) : im (bit0 z) = bit0 (im z) :=
   map_bit0 _ _
 #align is_R_or_C.bit0_im IsROrC.bit0_im
@@ -331,7 +331,7 @@ theorem I_im' (z : K) : im (I : K) * im z = im z := by rw [mul_comm, I_im]
 set_option linter.uppercaseLean3 false in
 #align is_R_or_C.I_im' IsROrC.I_im'
 
-@[isROrC_simps] -- porting note: was `simp`
+@[isROrC_simps] -- porting note (#10618): was `simp`
 theorem I_mul_re (z : K) : re (I * z) = -im z := by
   simp only [I_re, zero_sub, I_im', zero_mul, mul_re]
 set_option linter.uppercaseLean3 false in
@@ -369,13 +369,13 @@ theorem conj_ofReal (r : ℝ) : conj (r : K) = (r : K) := by
 #align is_R_or_C.conj_of_real IsROrC.conj_ofReal
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- porting note: was `simp` but `simp` can prove it
+@[deprecated, isROrC_simps] -- porting note (#10618): was `simp` but `simp` can prove it
 theorem conj_bit0 (z : K) : conj (bit0 z) = bit0 (conj z) :=
   map_bit0 _ _
 #align is_R_or_C.conj_bit0 IsROrC.conj_bit0
 
 set_option linter.deprecated false in
-@[deprecated, isROrC_simps] -- porting note: was `simp` but `simp` can prove it
+@[deprecated, isROrC_simps] -- porting note (#10618): was `simp` but `simp` can prove it
 theorem conj_bit1 (z : K) : conj (bit1 z) = bit1 (conj z) :=
   map_bit1 _ _
 #align is_R_or_C.conj_bit1 IsROrC.conj_bit1
@@ -495,7 +495,7 @@ theorem normSq_nonneg (z : K) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
 #align is_R_or_C.norm_sq_nonneg IsROrC.normSq_nonneg
 
-@[isROrC_simps] -- porting note: was `simp`
+@[isROrC_simps] -- porting note (#10618): was `simp`
 theorem normSq_eq_zero {z : K} : normSq z = 0 ↔ z = 0 :=
   map_eq_zero _
 #align is_R_or_C.norm_sq_eq_zero IsROrC.normSq_eq_zero
@@ -514,7 +514,7 @@ theorem normSq_conj (z : K) : normSq (conj z) = normSq z := by
   simp only [normSq_apply, neg_mul, mul_neg, neg_neg, isROrC_simps]
 #align is_R_or_C.norm_sq_conj IsROrC.normSq_conj
 
-@[isROrC_simps] -- porting note: was `simp`
+@[isROrC_simps] -- porting note (#10618): was `simp`
 theorem normSq_mul (z w : K) : normSq (z * w) = normSq z * normSq w :=
   map_mul _ z w
 #align is_R_or_C.norm_sq_mul IsROrC.normSq_mul
@@ -586,7 +586,7 @@ theorem div_im (z w : K) : im (z / w) = im z * re w / normSq w - re z * im w / n
     isROrC_simps]
 #align is_R_or_C.div_im IsROrC.div_im
 
-@[isROrC_simps] -- porting note: was `simp`
+@[isROrC_simps] -- porting note (#10618): was `simp`
 theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align is_R_or_C.conj_inv IsROrC.conj_inv
@@ -636,17 +636,17 @@ theorem div_I (z : K) : z / I = -(z * I) := by rw [div_eq_mul_inv, inv_I, mul_ne
 set_option linter.uppercaseLean3 false in
 #align is_R_or_C.div_I IsROrC.div_I
 
-@[isROrC_simps] -- porting note: was `simp`
+@[isROrC_simps] -- porting note (#10618): was `simp`
 theorem normSq_inv (z : K) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ normSq z
 #align is_R_or_C.norm_sq_inv IsROrC.normSq_inv
 
-@[isROrC_simps] -- porting note: was `simp`
+@[isROrC_simps] -- porting note (#10618): was `simp`
 theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w
 #align is_R_or_C.norm_sq_div IsROrC.normSq_div
 
-@[isROrC_simps] -- porting note: was `simp`
+@[isROrC_simps] -- porting note (#10618): was `simp`
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_normSq_eq_norm, normSq_conj]
 #align is_R_or_C.norm_conj IsROrC.norm_conj
 

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

@@ -1136,7 +1136,7 @@ theorem ofRealCLM_apply : (ofRealCLM : ℝ → K) = ofReal :=
   rfl
 #align is_R_or_C.of_real_clm_apply IsROrC.ofRealCLM_apply
 
-@[continuity]
+@[continuity, fun_prop]
 theorem continuous_ofReal : Continuous (ofReal : ℝ → K) :=
   ofRealLI.continuous
 #align is_R_or_C.continuous_of_real IsROrC.continuous_ofReal

@@ -6,6 +6,7 @@ Authors: Frédéric Dupuis
 import Mathlib.Data.Real.Sqrt
 import Mathlib.Analysis.NormedSpace.Star.Basic
 import Mathlib.Analysis.NormedSpace.ContinuousLinearMap
+import Mathlib.Analysis.NormedSpace.Basic
 
 #align_import data.is_R_or_C.basic from "leanprover-community/mathlib"@"baa88307f3e699fa7054ef04ec79fa4f056169cb"
 

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.

@@ -999,25 +999,25 @@ theorem reLm_coe : (reLm : K → ℝ) = re :=
 #align is_R_or_C.re_lm_coe IsROrC.reLm_coe
 
 /-- The real part in an `IsROrC` field, as a continuous linear map. -/
-noncomputable def reClm : K →L[ℝ] ℝ :=
+noncomputable def reCLM : K →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by
     rw [one_mul]
     exact abs_re_le_norm x
-#align is_R_or_C.re_clm IsROrC.reClm
+#align is_R_or_C.re_clm IsROrC.reCLM
 
 @[simp, isROrC_simps, norm_cast]
-theorem reClm_coe : ((reClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
+theorem reCLM_coe : ((reCLM : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = reLm :=
   rfl
-#align is_R_or_C.re_clm_coe IsROrC.reClm_coe
+#align is_R_or_C.re_clm_coe IsROrC.reCLM_coe
 
 @[simp, isROrC_simps]
-theorem reClm_apply : ((reClm : K →L[ℝ] ℝ) : K → ℝ) = re :=
+theorem reCLM_apply : ((reCLM : K →L[ℝ] ℝ) : K → ℝ) = re :=
   rfl
-#align is_R_or_C.re_clm_apply IsROrC.reClm_apply
+#align is_R_or_C.re_clm_apply IsROrC.reCLM_apply
 
 @[continuity]
 theorem continuous_re : Continuous (re : K → ℝ) :=
-  reClm.continuous
+  reCLM.continuous
 #align is_R_or_C.continuous_re IsROrC.continuous_re
 
 /-- The imaginary part in an `IsROrC` field, as a linear map. -/
@@ -1031,25 +1031,25 @@ theorem imLm_coe : (imLm : K → ℝ) = im :=
 #align is_R_or_C.im_lm_coe IsROrC.imLm_coe
 
 /-- The imaginary part in an `IsROrC` field, as a continuous linear map. -/
-noncomputable def imClm : K →L[ℝ] ℝ :=
+noncomputable def imCLM : K →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by
     rw [one_mul]
     exact abs_im_le_norm x
-#align is_R_or_C.im_clm IsROrC.imClm
+#align is_R_or_C.im_clm IsROrC.imCLM
 
 @[simp, isROrC_simps, norm_cast]
-theorem imClm_coe : ((imClm : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
+theorem imCLM_coe : ((imCLM : K →L[ℝ] ℝ) : K →ₗ[ℝ] ℝ) = imLm :=
   rfl
-#align is_R_or_C.im_clm_coe IsROrC.imClm_coe
+#align is_R_or_C.im_clm_coe IsROrC.imCLM_coe
 
 @[simp, isROrC_simps]
-theorem imClm_apply : ((imClm : K →L[ℝ] ℝ) : K → ℝ) = im :=
+theorem imCLM_apply : ((imCLM : K →L[ℝ] ℝ) : K → ℝ) = im :=
   rfl
-#align is_R_or_C.im_clm_apply IsROrC.imClm_apply
+#align is_R_or_C.im_clm_apply IsROrC.imCLM_apply
 
 @[continuity]
 theorem continuous_im : Continuous (im : K → ℝ) :=
-  imClm.continuous
+  imCLM.continuous
 #align is_R_or_C.continuous_im IsROrC.continuous_im
 
 /-- Conjugate as an `ℝ`-algebra equivalence -/
@@ -1067,32 +1067,32 @@ theorem conjAe_coe : (conjAe : K → K) = conj :=
 #align is_R_or_C.conj_ae_coe IsROrC.conjAe_coe
 
 /-- Conjugate as a linear isometry -/
-noncomputable def conjLie : K ≃ₗᵢ[ℝ] K :=
+noncomputable def conjLIE : K ≃ₗᵢ[ℝ] K :=
   ⟨conjAe.toLinearEquiv, fun _ => norm_conj⟩
-#align is_R_or_C.conj_lie IsROrC.conjLie
+#align is_R_or_C.conj_lie IsROrC.conjLIE
 
 @[simp, isROrC_simps]
-theorem conjLie_apply : (conjLie : K → K) = conj :=
+theorem conjLIE_apply : (conjLIE : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_lie_apply IsROrC.conjLie_apply
+#align is_R_or_C.conj_lie_apply IsROrC.conjLIE_apply
 
 /-- Conjugate as a continuous linear equivalence -/
-noncomputable def conjCle : K ≃L[ℝ] K :=
-  @conjLie K _
-#align is_R_or_C.conj_cle IsROrC.conjCle
+noncomputable def conjCLE : K ≃L[ℝ] K :=
+  @conjLIE K _
+#align is_R_or_C.conj_cle IsROrC.conjCLE
 
 @[simp, isROrC_simps]
-theorem conjCle_coe : (@conjCle K _).toLinearEquiv = conjAe.toLinearEquiv :=
+theorem conjCLE_coe : (@conjCLE K _).toLinearEquiv = conjAe.toLinearEquiv :=
   rfl
-#align is_R_or_C.conj_cle_coe IsROrC.conjCle_coe
+#align is_R_or_C.conj_cle_coe IsROrC.conjCLE_coe
 
 @[simp, isROrC_simps]
-theorem conjCle_apply : (conjCle : K → K) = conj :=
+theorem conjCLE_apply : (conjCLE : K → K) = conj :=
   rfl
-#align is_R_or_C.conj_cle_apply IsROrC.conjCle_apply
+#align is_R_or_C.conj_cle_apply IsROrC.conjCLE_apply
 
 instance (priority := 100) : ContinuousStar K :=
-  ⟨conjLie.continuous⟩
+  ⟨conjLIE.continuous⟩
 
 @[continuity]
 theorem continuous_conj : Continuous (conj : K → K) :=
@@ -1110,34 +1110,34 @@ theorem ofRealAm_coe : (ofRealAm : ℝ → K) = ofReal :=
 #align is_R_or_C.of_real_am_coe IsROrC.ofRealAm_coe
 
 /-- The ℝ → K coercion, as a linear isometry -/
-noncomputable def ofRealLi : ℝ →ₗᵢ[ℝ] K where
+noncomputable def ofRealLI : ℝ →ₗᵢ[ℝ] K where
   toLinearMap := ofRealAm.toLinearMap
   norm_map' := norm_ofReal
-#align is_R_or_C.of_real_li IsROrC.ofRealLi
+#align is_R_or_C.of_real_li IsROrC.ofRealLI
 
 @[simp, isROrC_simps]
-theorem ofRealLi_apply : (ofRealLi : ℝ → K) = ofReal :=
+theorem ofRealLI_apply : (ofRealLI : ℝ → K) = ofReal :=
   rfl
-#align is_R_or_C.of_real_li_apply IsROrC.ofRealLi_apply
+#align is_R_or_C.of_real_li_apply IsROrC.ofRealLI_apply
 
 /-- The `ℝ → K` coercion, as a continuous linear map -/
-noncomputable def ofRealClm : ℝ →L[ℝ] K :=
-  ofRealLi.toContinuousLinearMap
-#align is_R_or_C.of_real_clm IsROrC.ofRealClm
+noncomputable def ofRealCLM : ℝ →L[ℝ] K :=
+  ofRealLI.toContinuousLinearMap
+#align is_R_or_C.of_real_clm IsROrC.ofRealCLM
 
 @[simp, isROrC_simps]
-theorem ofRealClm_coe : (@ofRealClm K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinearMap :=
+theorem ofRealCLM_coe : (@ofRealCLM K _ : ℝ →ₗ[ℝ] K) = ofRealAm.toLinearMap :=
   rfl
-#align is_R_or_C.of_real_clm_coe IsROrC.ofRealClm_coe
+#align is_R_or_C.of_real_clm_coe IsROrC.ofRealCLM_coe
 
 @[simp, isROrC_simps]
-theorem ofRealClm_apply : (ofRealClm : ℝ → K) = ofReal :=
+theorem ofRealCLM_apply : (ofRealCLM : ℝ → K) = ofReal :=
   rfl
-#align is_R_or_C.of_real_clm_apply IsROrC.ofRealClm_apply
+#align is_R_or_C.of_real_clm_apply IsROrC.ofRealCLM_apply
 
 @[continuity]
 theorem continuous_ofReal : Continuous (ofReal : ℝ → K) :=
-  ofRealLi.continuous
+  ofRealLI.continuous
 #align is_R_or_C.continuous_of_real IsROrC.continuous_ofReal
 
 @[continuity]

From LeanAPAP

@@ -733,6 +733,10 @@ theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n := by
 theorem norm_ofNat (n : ℕ) [n.AtLeastTwo] : ‖(no_index (OfNat.ofNat n) : K)‖ = OfNat.ofNat n :=
   norm_natCast n
 
+variable (K) in
+lemma norm_nsmul [NormedAddCommGroup E] [NormedSpace K E] (n : ℕ) (x : E) : ‖n • x‖ = n • ‖x‖ := by
+  rw [nsmul_eq_smul_cast K, norm_smul, IsROrC.norm_natCast, nsmul_eq_mul]
+
 theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [normSq_eq_def', sq]
 #align is_R_or_C.mul_self_norm IsROrC.mul_self_norm
 

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.

@@ -341,6 +341,10 @@ theorem I_mul_I : (I : K) = 0 ∨ (I : K) * I = -1 :=
 set_option linter.uppercaseLean3 false in
 #align is_R_or_C.I_mul_I IsROrC.I_mul_I
 
+variable (𝕜) in
+lemma I_eq_zero_or_im_I_eq_one : (I : K) = 0 ∨ im (I : K) = 1 :=
+  I_mul_I (K := K) |>.imp_right fun h ↦ by simpa [h] using (I_mul_re (I : K)).symm
+
 @[simp, isROrC_simps]
 theorem conj_re (z : K) : re (conj z) = re z :=
   IsROrC.conj_re_ax z
@@ -1139,4 +1143,35 @@ theorem continuous_normSq : Continuous (normSq : K → ℝ) :=
 
 end LinearMaps
 
+/-!
+### ℝ-dependent results
+
+Here we gather results that depend on whether `K` is `ℝ`.
+-/
+section CaseSpecific
+
+lemma im_eq_zero (h : I = (0 : K)) (z : K) : im z = 0 := by
+  rw [← re_add_im z, h]
+  simp
+
+/-- The natural isomorphism between `𝕜` satisfying `IsROrC 𝕜` and `ℝ` when `IsROrC.I = 0`. -/
+@[simps]
+def realRingEquiv (h : I = (0 : K)) : K ≃+* ℝ where
+  toFun := re
+  invFun := (↑)
+  left_inv x := by nth_rw 2 [← re_add_im x]; simp [h]
+  right_inv := ofReal_re
+  map_add' := map_add re
+  map_mul' := by simp [im_eq_zero h]
+
+/-- The natural `ℝ`-linear isometry equivalence between `𝕜` satisfying `IsROrC 𝕜` and `ℝ` when
+`IsROrC.I = 0`. -/
+@[simps]
+noncomputable def realLinearIsometryEquiv (h : I = (0 : K)) : K ≃ₗᵢ[ℝ] ℝ where
+  map_smul' := smul_re
+  norm_map' z := by rw [← re_add_im z]; simp [- re_add_im, h]
+  __ := realRingEquiv h
+
+end CaseSpecific
+
 end IsROrC

and rename ofReal_mul_re → re_mul_ofReal, ofReal_mul_im → im_mul_ofReal.

From LeanAPAP

@@ -277,23 +277,23 @@ theorem real_smul_ofReal (r x : ℝ) : r • (x : K) = (r : K) * (x : K) :=
 #align is_R_or_C.real_smul_of_real IsROrC.real_smul_ofReal
 
 @[isROrC_simps]
-theorem ofReal_mul_re (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
+theorem re_ofReal_mul (r : ℝ) (z : K) : re (↑r * z) = r * re z := by
   simp only [mul_re, ofReal_im, zero_mul, ofReal_re, sub_zero]
-#align is_R_or_C.of_real_mul_re IsROrC.ofReal_mul_re
+#align is_R_or_C.of_real_mul_re IsROrC.re_ofReal_mul
 
 @[isROrC_simps]
-theorem ofReal_mul_im (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
+theorem im_ofReal_mul (r : ℝ) (z : K) : im (↑r * z) = r * im z := by
   simp only [add_zero, ofReal_im, zero_mul, ofReal_re, mul_im]
-#align is_R_or_C.of_real_mul_im IsROrC.ofReal_mul_im
+#align is_R_or_C.of_real_mul_im IsROrC.im_ofReal_mul
 
 @[isROrC_simps]
 theorem smul_re (r : ℝ) (z : K) : re (r • z) = r * re z := by
-  rw [real_smul_eq_coe_mul, ofReal_mul_re]
+  rw [real_smul_eq_coe_mul, re_ofReal_mul]
 #align is_R_or_C.smul_re IsROrC.smul_re
 
 @[isROrC_simps]
 theorem smul_im (r : ℝ) (z : K) : im (r • z) = r * im z := by
-  rw [real_smul_eq_coe_mul, ofReal_mul_im]
+  rw [real_smul_eq_coe_mul, im_ofReal_mul]
 #align is_R_or_C.smul_im IsROrC.smul_im
 
 @[simp, norm_cast, isROrC_simps]
@@ -563,12 +563,12 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) := by
 
 @[simp, isROrC_simps]
 theorem inv_re (z : K) : re z⁻¹ = re z / normSq z := by
-  rw [inv_def, normSq_eq_def', mul_comm, ofReal_mul_re, conj_re, div_eq_inv_mul]
+  rw [inv_def, normSq_eq_def', mul_comm, re_ofReal_mul, conj_re, div_eq_inv_mul]
 #align is_R_or_C.inv_re IsROrC.inv_re
 
 @[simp, isROrC_simps]
 theorem inv_im (z : K) : im z⁻¹ = -im z / normSq z := by
-  rw [inv_def, normSq_eq_def', mul_comm, ofReal_mul_im, conj_im, div_eq_inv_mul]
+  rw [inv_def, normSq_eq_def', mul_comm, im_ofReal_mul, conj_im, div_eq_inv_mul]
 #align is_R_or_C.inv_im IsROrC.inv_im
 
 theorem div_re (z w : K) : re (z / w) = re z * re w / normSq w + im z * im w / normSq w := by
@@ -605,7 +605,7 @@ theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
 #align is_R_or_C.of_real_div IsROrC.ofReal_div
 
 theorem div_re_ofReal {z : K} {r : ℝ} : re (z / r) = re z / r := by
-  rw [div_eq_inv_mul, div_eq_inv_mul, ← ofReal_inv, ofReal_mul_re]
+  rw [div_eq_inv_mul, div_eq_inv_mul, ← ofReal_inv, re_ofReal_mul]
 #align is_R_or_C.div_re_of_real IsROrC.div_re_ofReal
 
 @[simp, norm_cast, isROrC_simps]
@@ -681,11 +681,11 @@ theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
 
 theorem ofNat_mul_re (n : ℕ) [n.AtLeastTwo] (z : K) :
     re (OfNat.ofNat n * z) = OfNat.ofNat n * re z := by
-  rw [← ofReal_ofNat, ofReal_mul_re]
+  rw [← ofReal_ofNat, re_ofReal_mul]
 
 theorem ofNat_mul_im (n : ℕ) [n.AtLeastTwo] (z : K) :
     im (OfNat.ofNat n * z) = OfNat.ofNat n * im z := by
-  rw [← ofReal_ofNat, ofReal_mul_im]
+  rw [← ofReal_ofNat, im_ofReal_mul]
 
 @[simp, isROrC_simps, norm_cast]
 theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : K) = n :=

and other simple lemmas

From LeanAPAP

@@ -452,7 +452,7 @@ abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
   starRingEquiv
 #align is_R_or_C.conj_to_ring_equiv IsROrC.conjToRingEquiv
 
-variable {K}
+variable {K} {z : K}
 
 /-- The norm squared function. -/
 def normSq : K →*₀ ℝ where
@@ -527,13 +527,17 @@ theorem im_sq_le_normSq (z : K) : im z * im z ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
 #align is_R_or_C.im_sq_le_norm_sq IsROrC.im_sq_le_normSq
 
-theorem mul_conj (z : K) : z * conj z = (normSq z : K) := by
-  apply ext <;> simp only [normSq_apply, isROrC_simps, map_add, mul_zero] <;> ring
+theorem mul_conj (z : K) : z * conj z = ‖z‖ ^ 2 := by
+  apply ext <;> simp [← ofReal_pow, norm_sq_eq_def, mul_comm]
+
 #align is_R_or_C.mul_conj IsROrC.mul_conj
 
-theorem conj_mul (x : K) : conj x * x = (normSq x : K) := by rw [mul_comm, mul_conj]
+theorem conj_mul (z : K) : conj z * z = ‖z‖ ^ 2 := by rw [mul_comm, mul_conj]
 #align is_R_or_C.conj_mul IsROrC.conj_mul
 
+lemma inv_eq_conj (hz : ‖z‖ = 1) : z⁻¹ = conj z :=
+  inv_eq_of_mul_eq_one_left $ by simp_rw [conj_mul, hz, algebraMap.coe_one, one_pow]
+
 theorem normSq_sub (z w : K) : normSq (z - w) = normSq z + normSq w - 2 * re (z * conj w) := by
   simp only [normSq_add, sub_eq_add_neg, map_neg, mul_neg, normSq_neg, map_neg]
 #align is_R_or_C.norm_sq_sub IsROrC.normSq_sub
@@ -553,8 +557,8 @@ theorem inv_def (z : K) : z⁻¹ = conj z * ((‖z‖ ^ 2)⁻¹ : ℝ) := by
   rcases eq_or_ne z 0 with (rfl | h₀)
   · simp
   · apply inv_eq_of_mul_eq_one_right
-    rw [← mul_assoc, mul_conj, ofReal_inv, ← normSq_eq_def', mul_inv_cancel]
-    rwa [ofReal_ne_zero, Ne.def, normSq_eq_zero]
+    rw [← mul_assoc, mul_conj, ofReal_inv, ofReal_pow, mul_inv_cancel]
+    simpa
 #align is_R_or_C.inv_def IsROrC.inv_def
 
 @[simp, isROrC_simps]
@@ -582,6 +586,19 @@ theorem conj_inv (x : K) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align is_R_or_C.conj_inv IsROrC.conj_inv
 
+lemma conj_div (x y : K) : conj (x / y) = conj x / conj y := map_div' conj conj_inv _ _
+
+--TODO: Do we rather want the map as an explicit definition?
+lemma exists_norm_eq_mul_self (x : K) : ∃ c, ‖c‖ = 1 ∧ ↑‖x‖ = c * x := by
+  obtain rfl | hx := eq_or_ne x 0
+  · exact ⟨1, by simp⟩
+  · exact ⟨‖x‖ / x, by simp [norm_ne_zero_iff.2, hx]⟩
+
+lemma exists_norm_mul_eq_self (x : K) : ∃ c, ‖c‖ = 1 ∧ c * ‖x‖ = x := by
+  obtain rfl | hx := eq_or_ne x 0
+  · exact ⟨1, by simp⟩
+  · exact ⟨x / ‖x‖, by simp [norm_ne_zero_iff.2, hx]⟩
+
 @[simp, norm_cast, isROrC_simps]
 theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : K) = r / s :=
   map_div₀ (algebraMap ℝ K) r s
@@ -775,7 +792,7 @@ set_option linter.uppercaseLean3 false in
 #align is_R_or_C.norm_I_of_ne_zero IsROrC.norm_I_of_ne_zero
 
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
-  rw [mul_conj, ofReal_re, norm_ofReal, abs_of_nonneg (normSq_nonneg _)]
+  rw [mul_conj, ← ofReal_pow]; simp [-ofReal_pow]
 #align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj
 
 theorem norm_sq_re_add_conj (x : K) : ‖x + conj x‖ ^ 2 = re (x + conj x) ^ 2 := by
@@ -845,8 +862,9 @@ namespace IsROrC
 section Order
 
 open scoped ComplexOrder
+variable {z w : K}
 
-theorem lt_iff_re_im {z w : K} : z < w ↔ re z < re w ∧ im z = im w := by
+theorem lt_iff_re_im : z < w ↔ re z < re w ∧ im z = im w := by
   simp_rw [lt_iff_le_and_ne, @IsROrC.le_iff_re_im K]
   constructor
   · rintro ⟨⟨hr, hi⟩, heq⟩
@@ -854,18 +872,30 @@ theorem lt_iff_re_im {z w : K} : z < w ↔ re z < re w ∧ im z = im w := by
   · rintro ⟨⟨hr, hrn⟩, hi⟩
     exact ⟨⟨hr, hi⟩, ne_of_apply_ne _ hrn⟩
 
-theorem nonneg_iff {z : K} : 0 ≤ z ↔ 0 ≤ re z ∧ im z = 0 := by
+theorem nonneg_iff : 0 ≤ z ↔ 0 ≤ re z ∧ im z = 0 := by
   simpa only [map_zero, eq_comm] using le_iff_re_im (z := 0) (w := z)
 
-theorem pos_iff {z : K} : 0 < z ↔ 0 < re z ∧ im z = 0 := by
+theorem pos_iff : 0 < z ↔ 0 < re z ∧ im z = 0 := by
   simpa only [map_zero, eq_comm] using lt_iff_re_im (z := 0) (w := z)
 
-theorem nonpos_iff {z : K} : z ≤ 0 ↔ re z ≤ 0 ∧ im z = 0 := by
+theorem nonpos_iff : z ≤ 0 ↔ re z ≤ 0 ∧ im z = 0 := by
   simpa only [map_zero] using le_iff_re_im (z := z) (w := 0)
 
-theorem neg_iff {z : K} : z < 0 ↔ re z < 0 ∧ im z = 0 := by
+theorem neg_iff : z < 0 ↔ re z < 0 ∧ im z = 0 := by
   simpa only [map_zero] using lt_iff_re_im (z := z) (w := 0)
 
+lemma nonneg_iff_exists_ofReal : 0 ≤ z ↔ ∃ x ≥ (0 : ℝ), x = z := by
+  simp_rw [nonneg_iff (K := K), ext_iff (K := K)]; aesop
+
+lemma pos_iff_exists_ofReal : 0 < z ↔ ∃ x > (0 : ℝ), x = z := by
+  simp_rw [pos_iff (K := K), ext_iff (K := K)]; aesop
+
+lemma nonpos_iff_exists_ofReal : z ≤ 0 ↔ ∃ x ≤ (0 : ℝ), x = z := by
+  simp_rw [nonpos_iff (K := K), ext_iff (K := K)]; aesop
+
+lemma neg_iff_exists_ofReal : z < 0 ↔ ∃ x < (0 : ℝ), x = z := by
+  simp_rw [neg_iff (K := K), ext_iff (K := K)]; aesop
+
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℝ` and `ℂ` are star ordered rings.
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 
@@ -876,16 +906,10 @@ def toStarOrderedRing : StarOrderedRing K :=
       rw [IsROrC.le_iff_re_im] at *
       simpa [map_add, add_le_add_iff_left, add_right_inj] using hxy)
     (h_nonneg_iff := fun x => by
-      rw [IsROrC.le_iff_re_im, map_zero, map_zero, IsROrC.star_def, eq_comm]
-      constructor
-      · rintro ⟨hr, hi⟩
-        refine ⟨Real.sqrt (IsROrC.re x), ?_⟩
-        have := (IsROrC.is_real_TFAE x).out 2 3
-        rw [IsROrC.conj_ofReal, ← IsROrC.ofReal_mul, Real.mul_self_sqrt hr, eq_comm, this, hi]
-      · rintro ⟨s, rfl⟩
-        simp only [IsROrC.star_def, IsROrC.conj_mul]
-        rw [IsROrC.ofReal_re, IsROrC.ofReal_im, eq_self, and_true]
-        apply IsROrC.normSq_nonneg)
+      rw [nonneg_iff]
+      refine ⟨fun h ↦ ⟨(re x).sqrt, by simp [ext_iff (K := K), h.1, h.2]⟩, ?_⟩
+      rintro ⟨s, rfl⟩
+      simp [mul_comm, mul_self_nonneg, add_nonneg])
 
 scoped[ComplexOrder] attribute [instance] IsROrC.toStarOrderedRing
 

and other basic star lemmas

From LeanAPAP

@@ -932,7 +932,7 @@ theorem im_to_real {x : ℝ} : imR x = 0 :=
   rfl
 #align is_R_or_C.im_to_real IsROrC.im_to_real
 
-@[simp, isROrC_simps]
+@[isROrC_simps]
 theorem conj_to_real {x : ℝ} : conj x = x :=
   rfl
 #align is_R_or_C.conj_to_real IsROrC.conj_to_real

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -830,11 +830,11 @@ noncomputable instance Real.isROrC : IsROrC ℝ where
   mul_re_ax z w := by simp only [sub_zero, mul_zero, AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
   mul_im_ax z w := by simp only [add_zero, zero_mul, mul_zero, AddMonoidHom.zero_apply]
   conj_re_ax z := by simp only [starRingEnd_apply, star_id_of_comm]
-  conj_im_ax z := by simp only [neg_zero, AddMonoidHom.zero_apply]
+  conj_im_ax _ := by simp only [neg_zero, AddMonoidHom.zero_apply]
   conj_I_ax := by simp only [RingHom.map_zero, neg_zero]
   norm_sq_eq_def_ax z := by simp only [sq, Real.norm_eq_abs, ← abs_mul, abs_mul_self z, add_zero,
     mul_zero, AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
-  mul_im_I_ax z := by simp only [mul_zero, AddMonoidHom.zero_apply]
+  mul_im_I_ax _ := by simp only [mul_zero, AddMonoidHom.zero_apply]
   le_iff_re_im := (and_iff_left rfl).symm
 #align real.is_R_or_C Real.isROrC
 

Co-authored-by: timotree3 <timorcb@gmail.com>

@@ -646,14 +646,17 @@ theorem natCast_re (n : ℕ) : re (n : K) = n := by rw [← ofReal_natCast, ofRe
 theorem natCast_im (n : ℕ) : im (n : K) = 0 := by rw [← ofReal_natCast, ofReal_im]
 #align is_R_or_C.nat_cast_im IsROrC.natCast_im
 
+-- See note [no_index around OfNat.ofNat]
 @[simp, isROrC_simps]
 theorem ofNat_re (n : ℕ) [n.AtLeastTwo] : re (no_index (OfNat.ofNat n) : K) = OfNat.ofNat n :=
   natCast_re n
 
+-- See note [no_index around OfNat.ofNat]
 @[simp, isROrC_simps]
 theorem ofNat_im (n : ℕ) [n.AtLeastTwo] : im (no_index (OfNat.ofNat n) : K) = 0 :=
   natCast_im n
 
+-- See note [no_index around OfNat.ofNat]
 @[simp, isROrC_simps, norm_cast]
 theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
     ((no_index (OfNat.ofNat n) : ℝ) : K) = OfNat.ofNat n :=

We already have noncomputable DecidableEq instances for Real and Complex; putting them here too reduces friction in code generalized to IsROrC K.

@@ -74,9 +74,12 @@ class IsROrC (K : semiOutParam (Type*)) extends DenselyNormedField K, StarRing K
   /-- only an instance in the `ComplexOrder` locale -/
   [toPartialOrder : PartialOrder K]
   le_iff_re_im : z ≤ w ↔ re z ≤ re w ∧ im z = im w
+  -- note we cannot put this in the `extends` clause
+  [toDecidableEq : DecidableEq K]
 #align is_R_or_C IsROrC
 
 scoped[ComplexOrder] attribute [instance 100] IsROrC.toPartialOrder
+attribute [instance 100] IsROrC.toDecidableEq
 
 end
 

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -414,11 +414,11 @@ open List in
 theorem is_real_TFAE (z : K) : TFAE [conj z = z, ∃ r : ℝ, (r : K) = z, ↑(re z) = z, im z = 0] := by
   tfae_have 1 → 4
   · intro h
-    rw [← @ofReal_inj K, im_eq_conj_sub, h, sub_self, MulZeroClass.mul_zero, zero_div,
+    rw [← @ofReal_inj K, im_eq_conj_sub, h, sub_self, mul_zero, zero_div,
       ofReal_zero]
   tfae_have 4 → 3
   · intro h
-    conv_rhs => rw [← re_add_im z, h, ofReal_zero, MulZeroClass.zero_mul, add_zero]
+    conv_rhs => rw [← re_add_im z, h, ofReal_zero, zero_mul, add_zero]
   tfae_have 3 → 2; exact fun h => ⟨_, h⟩
   tfae_have 2 → 1; exact fun ⟨r, hr⟩ => hr ▸ conj_ofReal _
   tfae_finish
@@ -454,7 +454,7 @@ variable {K}
 /-- The norm squared function. -/
 def normSq : K →*₀ ℝ where
   toFun z := re z * re z + im z * im z
-  map_zero' := by simp only [add_zero, MulZeroClass.mul_zero, map_zero]
+  map_zero' := by simp only [add_zero, mul_zero, map_zero]
   map_one' := by simp only [one_im, add_zero, mul_one, one_re, mul_zero]
   map_mul' z w := by
     simp only [mul_im, mul_re]
@@ -828,7 +828,7 @@ noncomputable instance Real.isROrC : IsROrC ℝ where
   conj_I_ax := by simp only [RingHom.map_zero, neg_zero]
   norm_sq_eq_def_ax z := by simp only [sq, Real.norm_eq_abs, ← abs_mul, abs_mul_self z, add_zero,
     mul_zero, AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
-  mul_im_I_ax z := by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply]
+  mul_im_I_ax z := by simp only [mul_zero, AddMonoidHom.zero_apply]
   le_iff_re_im := (and_iff_left rfl).symm
 #align real.is_R_or_C Real.isROrC
 

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -39,6 +39,8 @@ their counterparts in `Mathlib/Analysis/Complex/Basic.lean` (which causes linter
 A few lemmas requiring heavier imports are in `Mathlib/Data/IsROrC/Lemmas.lean`.
 -/
 
+set_option autoImplicit true
+
 
 open BigOperators
 

@@ -23,20 +23,20 @@ typeclass, which basically amounts to doing the complex case, and the two cases
 immediately from the two instances of the class.
 
 The instance for `ℝ` is registered in this file.
-The instance for `ℂ` is declared in `analysis.complex.basic`.
+The instance for `ℂ` is declared in `Mathlib/Analysis/Complex/Basic.lean`.
 
 ## Implementation notes
 
-The coercion from reals into an `IsROrC` field is done by registering `algebraMap ℝ K` as
-a `CoeTCₓ`. For this to work, we must proceed carefully to avoid problems involving circular
+The coercion from reals into an `IsROrC` field is done by registering `IsROrC.ofReal` as
+a `CoeTC`. For this to work, we must proceed carefully to avoid problems involving circular
 coercions in the case `K=ℝ`; in particular, we cannot use the plain `Coe` and must set
 priorities carefully. This problem was already solved for `ℕ`, and we copy the solution detailed
-in `data/Nat/cast`. See also Note [coercion into rings] for more details.
+in `Mathlib/Data/Nat/Cast/Defs.lean`. See also Note [coercion into rings] for more details.
 
 In addition, several lemmas need to be set at priority 900 to make sure that they do not override
-their counterparts in `complex.lean` (which causes linter errors).
+their counterparts in `Mathlib/Analysis/Complex/Basic.lean` (which causes linter errors).
 
-A few lemmas requiring heavier imports are in `data.is_R_or_C.lemmas`.
+A few lemmas requiring heavier imports are in `Mathlib/Data/IsROrC/Lemmas.lean`.
 -/
 
 
@@ -88,7 +88,7 @@ open ComplexConjugate
 @[coe] abbrev ofReal : ℝ → K := Algebra.cast
 
 /- The priority must be set at 900 to ensure that coercions are tried in the right order.
-See Note [coercion into rings], or `data/nat/cast.lean` for more details. -/
+See Note [coercion into rings], or `Mathlib/Data/Nat/Cast/Basic.lean` for more details. -/
 noncomputable instance (priority := 900) algebraMapCoe : CoeTC ℝ K :=
   ⟨ofReal⟩
 #align is_R_or_C.algebra_map_coe IsROrC.algebraMapCoe

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

This has nice performance benefits.

@@ -51,7 +51,7 @@ open ComplexConjugate
 /--
 This typeclass captures properties shared by ℝ and ℂ, with an API that closely matches that of ℂ.
 -/
-class IsROrC (K : semiOutParam (Type _)) extends DenselyNormedField K, StarRing K,
+class IsROrC (K : semiOutParam (Type*)) extends DenselyNormedField K, StarRing K,
     NormedAlgebra ℝ K, CompleteSpace K where
   re : K →+ ℝ
   im : K →+ ℝ
@@ -78,7 +78,7 @@ scoped[ComplexOrder] attribute [instance 100] IsROrC.toPartialOrder
 
 end
 
-variable {K E : Type _} [IsROrC K]
+variable {K E : Type*} [IsROrC K]
 
 namespace IsROrC
 
@@ -233,13 +233,13 @@ theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : K) = r - s :=
 #align is_R_or_C.of_real_sub IsROrC.ofReal_sub
 
 @[simp, isROrC_simps, norm_cast]
-theorem ofReal_sum {α : Type _} (s : Finset α) (f : α → ℝ) :
+theorem ofReal_sum {α : Type*} (s : Finset α) (f : α → ℝ) :
     ((∑ i in s, f i : ℝ) : K) = ∑ i in s, (f i : K) :=
   map_sum (algebraMap ℝ K) _ _
 #align is_R_or_C.of_real_sum IsROrC.ofReal_sum
 
 @[simp, isROrC_simps, norm_cast]
-theorem ofReal_finsupp_sum {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
+theorem ofReal_finsupp_sum {α M : Type*} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.sum fun a b => g a b : ℝ) : K) = f.sum fun a b => (g a b : K) :=
   map_finsupp_sum (algebraMap ℝ K) f g
 #align is_R_or_C.of_real_finsupp_sum IsROrC.ofReal_finsupp_sum
@@ -255,13 +255,13 @@ theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = (r : K) ^ n :=
 #align is_R_or_C.of_real_pow IsROrC.ofReal_pow
 
 @[simp, isROrC_simps, norm_cast]
-theorem ofReal_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
+theorem ofReal_prod {α : Type*} (s : Finset α) (f : α → ℝ) :
     ((∏ i in s, f i : ℝ) : K) = ∏ i in s, (f i : K) :=
   map_prod (algebraMap ℝ K) _ _
 #align is_R_or_C.of_real_prod IsROrC.ofReal_prod
 
 @[simp, isROrC_simps, norm_cast]
-theorem ofReal_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
+theorem ofReal_finsupp_prod {α M : Type*} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.prod fun a b => g a b : ℝ) : K) = f.prod fun a b => (g a b : K) :=
   map_finsupp_prod _ f g
 #align is_R_or_C.of_real_finsupp_prod IsROrC.ofReal_finsupp_prod

@@ -846,6 +846,18 @@ theorem lt_iff_re_im {z w : K} : z < w ↔ re z < re w ∧ im z = im w := by
   · rintro ⟨⟨hr, hrn⟩, hi⟩
     exact ⟨⟨hr, hi⟩, ne_of_apply_ne _ hrn⟩
 
+theorem nonneg_iff {z : K} : 0 ≤ z ↔ 0 ≤ re z ∧ im z = 0 := by
+  simpa only [map_zero, eq_comm] using le_iff_re_im (z := 0) (w := z)
+
+theorem pos_iff {z : K} : 0 < z ↔ 0 < re z ∧ im z = 0 := by
+  simpa only [map_zero, eq_comm] using lt_iff_re_im (z := 0) (w := z)
+
+theorem nonpos_iff {z : K} : z ≤ 0 ↔ re z ≤ 0 ∧ im z = 0 := by
+  simpa only [map_zero] using le_iff_re_im (z := z) (w := 0)
+
+theorem neg_iff {z : K} : z < 0 ↔ re z < 0 ∧ im z = 0 := by
+  simpa only [map_zero] using lt_iff_re_im (z := z) (w := 0)
+
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℝ` and `ℂ` are star ordered rings.
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 

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>

@@ -69,8 +69,13 @@ class IsROrC (K : semiOutParam (Type _)) extends DenselyNormedField K, StarRing
   conj_I_ax : conj I = -I
   norm_sq_eq_def_ax : ∀ z : K, ‖z‖ ^ 2 = re z * re z + im z * im z
   mul_im_I_ax : ∀ z : K, im z * im I = im z
+  /-- only an instance in the `ComplexOrder` locale -/
+  [toPartialOrder : PartialOrder K]
+  le_iff_re_im : z ≤ w ↔ re z ≤ re w ∧ im z = im w
 #align is_R_or_C IsROrC
 
+scoped[ComplexOrder] attribute [instance 100] IsROrC.toPartialOrder
+
 end
 
 variable {K E : Type _} [IsROrC K]
@@ -822,12 +827,72 @@ noncomputable instance Real.isROrC : IsROrC ℝ where
   norm_sq_eq_def_ax z := by simp only [sq, Real.norm_eq_abs, ← abs_mul, abs_mul_self z, add_zero,
     mul_zero, AddMonoidHom.zero_apply, AddMonoidHom.id_apply]
   mul_im_I_ax z := by simp only [MulZeroClass.mul_zero, AddMonoidHom.zero_apply]
+  le_iff_re_im := (and_iff_left rfl).symm
 #align real.is_R_or_C Real.isROrC
 
 end Instances
 
 namespace IsROrC
 
+section Order
+
+open scoped ComplexOrder
+
+theorem lt_iff_re_im {z w : K} : z < w ↔ re z < re w ∧ im z = im w := by
+  simp_rw [lt_iff_le_and_ne, @IsROrC.le_iff_re_im K]
+  constructor
+  · rintro ⟨⟨hr, hi⟩, heq⟩
+    exact ⟨⟨hr, mt (fun hreq => ext hreq hi) heq⟩, hi⟩
+  · rintro ⟨⟨hr, hrn⟩, hi⟩
+    exact ⟨⟨hr, hi⟩, ne_of_apply_ne _ hrn⟩
+
+/-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℝ` and `ℂ` are star ordered rings.
+(That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
+
+Note this is only an instance with `open scoped ComplexOrder`. -/
+def toStarOrderedRing : StarOrderedRing K :=
+  StarOrderedRing.ofNonnegIff'
+    (h_add := fun {x y} hxy z => by
+      rw [IsROrC.le_iff_re_im] at *
+      simpa [map_add, add_le_add_iff_left, add_right_inj] using hxy)
+    (h_nonneg_iff := fun x => by
+      rw [IsROrC.le_iff_re_im, map_zero, map_zero, IsROrC.star_def, eq_comm]
+      constructor
+      · rintro ⟨hr, hi⟩
+        refine ⟨Real.sqrt (IsROrC.re x), ?_⟩
+        have := (IsROrC.is_real_TFAE x).out 2 3
+        rw [IsROrC.conj_ofReal, ← IsROrC.ofReal_mul, Real.mul_self_sqrt hr, eq_comm, this, hi]
+      · rintro ⟨s, rfl⟩
+        simp only [IsROrC.star_def, IsROrC.conj_mul]
+        rw [IsROrC.ofReal_re, IsROrC.ofReal_im, eq_self, and_true]
+        apply IsROrC.normSq_nonneg)
+
+scoped[ComplexOrder] attribute [instance] IsROrC.toStarOrderedRing
+
+/-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℝ` and `ℂ` are strictly ordered rings.
+
+Note this is only an instance with `open scoped ComplexOrder`. -/
+def toStrictOrderedCommRing : StrictOrderedCommRing K where
+  zero_le_one := by simp [@IsROrC.le_iff_re_im K]
+  add_le_add_left _ _ := add_le_add_left
+  mul_pos z w hz hw := by
+    rw [lt_iff_re_im, map_zero] at hz hw ⊢
+    simp [mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1]
+  mul_comm := by intros; apply ext <;> ring_nf
+
+scoped[ComplexOrder] attribute [instance] IsROrC.toStrictOrderedCommRing
+
+theorem toOrderedSMul : OrderedSMul ℝ K :=
+  OrderedSMul.mk' fun a b r hab hr => by
+    replace hab := hab.le
+    rw [IsROrC.le_iff_re_im] at hab
+    rw [IsROrC.le_iff_re_im, smul_re, smul_re, smul_im, smul_im]
+    exact hab.imp (fun h => mul_le_mul_of_nonneg_left h hr.le) (congr_arg _)
+
+scoped[ComplexOrder] attribute [instance] IsROrC.toOrderedSMul
+
+end Order
+
 open ComplexConjugate
 
 section CleanupLemmas

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
-
-! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit baa88307f3e699fa7054ef04ec79fa4f056169cb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Real.Sqrt
 import Mathlib.Analysis.NormedSpace.Star.Basic
 import Mathlib.Analysis.NormedSpace.ContinuousLinearMap
 
+#align_import data.is_R_or_C.basic from "leanprover-community/mathlib"@"baa88307f3e699fa7054ef04ec79fa4f056169cb"
+
 /-!
 # `IsROrC`: a typeclass for ℝ or ℂ
 

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit 48fb5b5280e7c81672afc9524185ae994553ebf4
+! leanprover-community/mathlib commit baa88307f3e699fa7054ef04ec79fa4f056169cb
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -758,6 +758,12 @@ theorem abs_im_div_norm_le_one (z : K) : |im z / ‖z‖| ≤ 1 := by
   exact div_le_one_of_le (abs_im_le_norm _) (norm_nonneg _)
 #align is_R_or_C.abs_im_div_norm_le_one IsROrC.abs_im_div_norm_le_one
 
+theorem norm_I_of_ne_zero (hI : (I : K) ≠ 0) : ‖(I : K)‖ = 1 := by
+  rw [← mul_self_inj_of_nonneg (norm_nonneg I) zero_le_one, one_mul, ← norm_mul,
+    I_mul_I_of_nonzero hI, norm_neg, norm_one]
+set_option linter.uppercaseLean3 false in
+#align is_R_or_C.norm_I_of_ne_zero IsROrC.norm_I_of_ne_zero
+
 theorem re_eq_norm_of_mul_conj (x : K) : re (x * conj x) = ‖x * conj x‖ := by
   rw [mul_conj, ofReal_re, norm_ofReal, abs_of_nonneg (normSq_nonneg _)]
 #align is_R_or_C.re_eq_norm_of_mul_conj IsROrC.re_eq_norm_of_mul_conj

• depends on: https://github.com/leanprover/std4/pull/163
• depends on: #5584
• depends on: #5715
• depends on: #5729
• depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -640,15 +640,16 @@ theorem natCast_im (n : ℕ) : im (n : K) = 0 := by rw [← ofReal_natCast, ofRe
 #align is_R_or_C.nat_cast_im IsROrC.natCast_im
 
 @[simp, isROrC_simps]
-theorem ofNat_re (n : ℕ) [n.AtLeastTwo] : re (OfNat.ofNat n : K) = OfNat.ofNat n :=
+theorem ofNat_re (n : ℕ) [n.AtLeastTwo] : re (no_index (OfNat.ofNat n) : K) = OfNat.ofNat n :=
   natCast_re n
 
 @[simp, isROrC_simps]
-theorem ofNat_im (n : ℕ) [n.AtLeastTwo] : im (OfNat.ofNat n : K) = 0 :=
+theorem ofNat_im (n : ℕ) [n.AtLeastTwo] : im (no_index (OfNat.ofNat n) : K) = 0 :=
   natCast_im n
 
 @[simp, isROrC_simps, norm_cast]
-theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] : ((OfNat.ofNat n : ℝ) : K) = OfNat.ofNat n :=
+theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
+    ((no_index (OfNat.ofNat n) : ℝ) : K) = OfNat.ofNat n :=
   ofReal_natCast n
 
 theorem ofNat_mul_re (n : ℕ) [n.AtLeastTwo] (z : K) :
@@ -698,7 +699,7 @@ theorem norm_natCast (n : ℕ) : ‖(n : K)‖ = n := by
 #align is_R_or_C.norm_nat_cast IsROrC.norm_natCast
 
 @[simp, isROrC_simps]
-theorem norm_ofNat (n : ℕ) [n.AtLeastTwo] : ‖(OfNat.ofNat n : K)‖ = OfNat.ofNat n :=
+theorem norm_ofNat (n : ℕ) [n.AtLeastTwo] : ‖(no_index (OfNat.ofNat n) : K)‖ = OfNat.ofNat n :=
   norm_natCast n
 
 theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [normSq_eq_def', sq]

There are slight differences between mathlib3 and mathlib4 (different set of attributes, different lemmas are in core/std), so I redid the same refactor instead of forward-porting changes.

mathlib3 PR: leanprover-community/mathlib#19223

@@ -4,12 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module data.is_R_or_C.basic
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
+! leanprover-community/mathlib commit 48fb5b5280e7c81672afc9524185ae994553ebf4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathlib.Data.Real.Sqrt
-import Mathlib.Data.IsROrC.Attr
 import Mathlib.Analysis.NormedSpace.Star.Basic
 import Mathlib.Analysis.NormedSpace.ContinuousLinearMap
 

Part 2 of #5001

@@ -868,7 +868,7 @@ end CleanupLemmas
 
 section LinearMaps
 
-/-- The real part in a `IsROrC` field, as a linear map. -/
+/-- The real part in an `IsROrC` field, as a linear map. -/
 def reLm : K →ₗ[ℝ] ℝ :=
   { re with map_smul' := smul_re }
 #align is_R_or_C.re_lm IsROrC.reLm
@@ -878,7 +878,7 @@ theorem reLm_coe : (reLm : K → ℝ) = re :=
   rfl
 #align is_R_or_C.re_lm_coe IsROrC.reLm_coe
 
-/-- The real part in a `IsROrC` field, as a continuous linear map. -/
+/-- The real part in an `IsROrC` field, as a continuous linear map. -/
 noncomputable def reClm : K →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by
     rw [one_mul]
@@ -900,7 +900,7 @@ theorem continuous_re : Continuous (re : K → ℝ) :=
   reClm.continuous
 #align is_R_or_C.continuous_re IsROrC.continuous_re
 
-/-- The imaginary part in a `IsROrC` field, as a linear map. -/
+/-- The imaginary part in an `IsROrC` field, as a linear map. -/
 def imLm : K →ₗ[ℝ] ℝ :=
   { im with map_smul' := smul_im }
 #align is_R_or_C.im_lm IsROrC.imLm
@@ -910,7 +910,7 @@ theorem imLm_coe : (imLm : K → ℝ) = im :=
   rfl
 #align is_R_or_C.im_lm_coe IsROrC.imLm_coe
 
-/-- The imaginary part in a `IsROrC` field, as a continuous linear map. -/
+/-- The imaginary part in an `IsROrC` field, as a continuous linear map. -/
 noncomputable def imClm : K →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by
     rw [one_mul]

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -14,9 +14,9 @@ import Mathlib.Analysis.NormedSpace.Star.Basic
 import Mathlib.Analysis.NormedSpace.ContinuousLinearMap
 
 /-!
-# `is_R_or_C`: a typeclass for ℝ or ℂ
+# `IsROrC`: a typeclass for ℝ or ℂ
 
-This file defines the typeclass `is_R_or_C` intended to have only two instances:
+This file defines the typeclass `IsROrC` intended to have only two instances:
 ℝ and ℂ. It is meant for definitions and theorems which hold for both the real and the complex case,
 and in particular when the real case follows directly from the complex case by setting `re` to `id`,
 `im` to zero and so on. Its API follows closely that of ℂ.
@@ -31,11 +31,11 @@ The instance for `ℂ` is declared in `analysis.complex.basic`.
 
 ## Implementation notes
 
-The coercion from reals into an `is_R_or_C` field is done by registering `algebra_map ℝ K` as
-a `has_coe_t`. For this to work, we must proceed carefully to avoid problems involving circular
-coercions in the case `K=ℝ`; in particular, we cannot use the plain `has_coe` and must set
+The coercion from reals into an `IsROrC` field is done by registering `algebraMap ℝ K` as
+a `CoeTCₓ`. For this to work, we must proceed carefully to avoid problems involving circular
+coercions in the case `K=ℝ`; in particular, we cannot use the plain `Coe` and must set
 priorities carefully. This problem was already solved for `ℕ`, and we copy the solution detailed
-in `data/nat/cast`. See also Note [coercion into rings] for more details.
+in `data/Nat/cast`. See also Note [coercion into rings] for more details.
 
 In addition, several lemmas need to be set at priority 900 to make sure that they do not override
 their counterparts in `complex.lean` (which causes linter errors).
@@ -868,7 +868,7 @@ end CleanupLemmas
 
 section LinearMaps
 
-/-- The real part in a `is_R_or_C` field, as a linear map. -/
+/-- The real part in a `IsROrC` field, as a linear map. -/
 def reLm : K →ₗ[ℝ] ℝ :=
   { re with map_smul' := smul_re }
 #align is_R_or_C.re_lm IsROrC.reLm
@@ -878,7 +878,7 @@ theorem reLm_coe : (reLm : K → ℝ) = re :=
   rfl
 #align is_R_or_C.re_lm_coe IsROrC.reLm_coe
 
-/-- The real part in a `is_R_or_C` field, as a continuous linear map. -/
+/-- The real part in a `IsROrC` field, as a continuous linear map. -/
 noncomputable def reClm : K →L[ℝ] ℝ :=
   reLm.mkContinuous 1 fun x => by
     rw [one_mul]
@@ -900,7 +900,7 @@ theorem continuous_re : Continuous (re : K → ℝ) :=
   reClm.continuous
 #align is_R_or_C.continuous_re IsROrC.continuous_re
 
-/-- The imaginary part in a `is_R_or_C` field, as a linear map. -/
+/-- The imaginary part in a `IsROrC` field, as a linear map. -/
 def imLm : K →ₗ[ℝ] ℝ :=
   { im with map_smul' := smul_im }
 #align is_R_or_C.im_lm IsROrC.imLm
@@ -910,7 +910,7 @@ theorem imLm_coe : (imLm : K → ℝ) = im :=
   rfl
 #align is_R_or_C.im_lm_coe IsROrC.imLm_coe
 
-/-- The imaginary part in a `is_R_or_C` field, as a continuous linear map. -/
+/-- The imaginary part in a `IsROrC` field, as a continuous linear map. -/
 noncomputable def imClm : K →L[ℝ] ℝ :=
   imLm.mkContinuous 1 fun x => by
     rw [one_mul]

I had to add big maxHeartbeats increases into two places, but I haven't been able to improve the situation (it compiles though). This might need to be addressed before merging.

Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>

@@ -55,8 +55,8 @@ open ComplexConjugate
 /--
 This typeclass captures properties shared by ℝ and ℂ, with an API that closely matches that of ℂ.
 -/
-class IsROrC (K : Type _) extends DenselyNormedField K, StarRing K, NormedAlgebra ℝ K,
-    CompleteSpace K where
+class IsROrC (K : semiOutParam (Type _)) extends DenselyNormedField K, StarRing K,
+    NormedAlgebra ℝ K, CompleteSpace K where
   re : K →+ ℝ
   im : K →+ ℝ
   /-- Imaginary unit in `K`. Meant to be set to `0` for `K = ℝ`. -/

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -433,8 +433,7 @@ theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
   (is_real_TFAE z).out 0 3
 #align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_im
 
--- porting note: @[simp] commented out because simpNF linter times out regardless of etaExperiment
--- @[simp]
+@[simp]
 theorem star_def : (Star.star : K → K) = conj :=
   rfl
 #align is_R_or_C.star_def IsROrC.star_def

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>

@@ -253,14 +253,12 @@ theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : K) = (r : K) ^ n :=
   map_pow (algebraMap ℝ K) r n
 #align is_R_or_C.of_real_pow IsROrC.ofReal_pow
 
-set_option synthInstance.etaExperiment true in -- porting note: lean4#2074
 @[simp, isROrC_simps, norm_cast]
 theorem ofReal_prod {α : Type _} (s : Finset α) (f : α → ℝ) :
     ((∏ i in s, f i : ℝ) : K) = ∏ i in s, (f i : K) :=
   map_prod (algebraMap ℝ K) _ _
 #align is_R_or_C.of_real_prod IsROrC.ofReal_prod
 
-set_option synthInstance.etaExperiment true in -- porting note: lean4#2074
 @[simp, isROrC_simps, norm_cast]
 theorem ofReal_finsupp_prod {α M : Type _} [Zero M] (f : α →₀ M) (g : α → M → ℝ) :
     ((f.prod fun a b => g a b : ℝ) : K) = f.prod fun a b => (g a b : K) :=
@@ -435,7 +433,6 @@ theorem conj_eq_iff_im {z : K} : conj z = z ↔ im z = 0 :=
   (is_real_TFAE z).out 0 3
 #align is_R_or_C.conj_eq_iff_im IsROrC.conj_eq_iff_im
 
-set_option synthInstance.etaExperiment true in
 -- porting note: @[simp] commented out because simpNF linter times out regardless of etaExperiment
 -- @[simp]
 theorem star_def : (Star.star : K → K) = conj :=
@@ -444,7 +441,6 @@ theorem star_def : (Star.star : K → K) = conj :=
 
 variable (K)
 
-set_option synthInstance.etaExperiment true in
 /-- Conjugation as a ring equivalence. This is used to convert the inner product into a
 sesquilinear product. -/
 abbrev conjToRingEquiv : K ≃+* Kᵐᵒᵖ :=
@@ -623,11 +619,10 @@ theorem normSq_div (z w : K) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w
 #align is_R_or_C.norm_sq_div IsROrC.normSq_div
 
-@[simp, isROrC_simps]
+@[isROrC_simps] -- porting note: was `simp`
 theorem norm_conj {z : K} : ‖conj z‖ = ‖z‖ := by simp only [← sqrt_normSq_eq_norm, normSq_conj]
 #align is_R_or_C.norm_conj IsROrC.norm_conj
 
-set_option synthInstance.etaExperiment true in
 instance (priority := 100) : CstarRing K where
   norm_star_mul_self {x} := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) norm_conj
 
@@ -666,7 +661,6 @@ theorem ofNat_mul_im (n : ℕ) [n.AtLeastTwo] (z : K) :
     im (OfNat.ofNat n * z) = OfNat.ofNat n * im z := by
   rw [← ofReal_ofNat, ofReal_mul_im]
 
-set_option synthInstance.etaExperiment true in -- porting note: lean4#2074
 @[simp, isROrC_simps, norm_cast]
 theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : K) = n :=
   map_intCast _ n
@@ -978,11 +972,9 @@ theorem conjCle_apply : (conjCle : K → K) = conj :=
   rfl
 #align is_R_or_C.conj_cle_apply IsROrC.conjCle_apply
 
-set_option synthInstance.etaExperiment true in
 instance (priority := 100) : ContinuousStar K :=
   ⟨conjLie.continuous⟩
 
-set_option synthInstance.etaExperiment true in
 @[continuity]
 theorem continuous_conj : Continuous (conj : K → K) :=
   continuous_star

Co-authored-by: Mauricio Collares <mauricio@collares.org>