analysis.complex.isometry ⟷ Mathlib.Analysis.Complex.Isometry

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

@@ -79,8 +79,8 @@ theorem rotation_ne_conjLIE (a : circle) : rotation a ≠ conjLIE :=
   intro h
   have h1 : rotation a 1 = conj 1 := LinearIsometryEquiv.congr_fun h 1
   have hI : rotation a I = conj I := LinearIsometryEquiv.congr_fun h I
-  rw [rotation_apply, RingHom.map_one, mul_one] at h1 
-  rw [rotation_apply, conj_I, ← neg_one_mul, mul_left_inj' I_ne_zero, h1, eq_neg_self_iff] at hI 
+  rw [rotation_apply, RingHom.map_one, mul_one] at h1
+  rw [rotation_apply, conj_I, ← neg_one_mul, mul_left_inj' I_ne_zero, h1, eq_neg_self_iff] at hI
   exact one_ne_zero hI
 #align rotation_ne_conj_lie rotation_ne_conjLIE
 -/
@@ -120,9 +120,9 @@ theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗ
     (h₂ : ∀ z, (f z).re = z.re) (z : ℂ) : (f z).im = z.im ∨ (f z).im = -z.im :=
   by
   have h₁ := f.norm_map z
-  simp only [Complex.abs_def, norm_eq_abs] at h₁ 
+  simp only [Complex.abs_def, norm_eq_abs] at h₁
   rwa [Real.sqrt_inj (norm_sq_nonneg _) (norm_sq_nonneg _), norm_sq_apply (f z), norm_sq_apply z,
-    h₂, add_left_cancel_iff, mul_self_eq_mul_self_iff] at h₁ 
+    h₂, add_left_cancel_iff, mul_self_eq_mul_self_iff] at h₁
 #align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re
 -/
 
@@ -131,15 +131,15 @@ theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
     z + conj z = f z + conj (f z) :=
   by
   have : ‖f z - 1‖ = ‖z - 1‖ := by rw [← f.norm_map (z - 1), f.map_sub, h]
-  apply_fun fun x => x ^ 2 at this 
-  simp only [norm_eq_abs, ← norm_sq_eq_abs] at this 
-  rw [← of_real_inj, ← mul_conj, ← mul_conj] at this 
-  rw [RingHom.map_sub, RingHom.map_sub] at this 
-  simp only [sub_mul, mul_sub, one_mul, mul_one] at this 
-  rw [mul_conj, norm_sq_eq_abs, ← norm_eq_abs, LinearIsometry.norm_map] at this 
-  rw [mul_conj, norm_sq_eq_abs, ← norm_eq_abs] at this 
-  simp only [sub_sub, sub_right_inj, mul_one, of_real_pow, RingHom.map_one, norm_eq_abs] at this 
-  simp only [add_sub, sub_left_inj] at this 
+  apply_fun fun x => x ^ 2 at this
+  simp only [norm_eq_abs, ← norm_sq_eq_abs] at this
+  rw [← of_real_inj, ← mul_conj, ← mul_conj] at this
+  rw [RingHom.map_sub, RingHom.map_sub] at this
+  simp only [sub_mul, mul_sub, one_mul, mul_one] at this
+  rw [mul_conj, norm_sq_eq_abs, ← norm_eq_abs, LinearIsometry.norm_map] at this
+  rw [mul_conj, norm_sq_eq_abs, ← norm_eq_abs] at this
+  simp only [sub_sub, sub_right_inj, mul_one, of_real_pow, RingHom.map_one, norm_eq_abs] at this
+  simp only [add_sub, sub_left_inj] at this
   rw [add_comm, ← this, add_comm]
 #align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_im
 -/

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

@@ -73,8 +73,8 @@ theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotati
 #align rotation_trans rotation_trans
 -/
 
-#print rotation_ne_conjLie /-
-theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
+#print rotation_ne_conjLIE /-
+theorem rotation_ne_conjLIE (a : circle) : rotation a ≠ conjLIE :=
   by
   intro h
   have h1 : rotation a 1 = conj 1 := LinearIsometryEquiv.congr_fun h 1
@@ -82,7 +82,7 @@ theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   rw [rotation_apply, RingHom.map_one, mul_one] at h1 
   rw [rotation_apply, conj_I, ← neg_one_mul, mul_left_inj' I_ne_zero, h1, eq_neg_self_iff] at hI 
   exact one_ne_zero hI
-#align rotation_ne_conj_lie rotation_ne_conjLie
+#align rotation_ne_conj_lie rotation_ne_conjLIE
 -/
 
 #print rotationOf /-
@@ -155,7 +155,7 @@ theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
 
 #print linear_isometry_complex_aux /-
 theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
-    f = LinearIsometryEquiv.refl ℝ ℂ ∨ f = conjLie :=
+    f = LinearIsometryEquiv.refl ℝ ℂ ∨ f = conjLIE :=
   by
   have h0 : f I = I ∨ f I = -I :=
     by
@@ -176,7 +176,7 @@ theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
 
 #print linear_isometry_complex /-
 theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
-    ∃ a : circle, f = rotation a ∨ f = conjLie.trans (rotation a) :=
+    ∃ a : circle, f = rotation a ∨ f = conjLIE.trans (rotation a) :=
   by
   let a : circle := ⟨f 1, by simpa using f.norm_map 1⟩
   use a

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 François Sunatori. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: François Sunatori
 -/
-import Mathbin.Analysis.Complex.Circle
-import Mathbin.LinearAlgebra.Determinant
-import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
+import Analysis.Complex.Circle
+import LinearAlgebra.Determinant
+import LinearAlgebra.Matrix.GeneralLinearGroup
 
 #align_import analysis.complex.isometry from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
 

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

@@ -48,7 +48,7 @@ def rotation : circle →* ℂ ≃ₗᵢ[ℝ] ℂ
     { DistribMulAction.toLinearEquiv ℝ ℂ a with
       norm_map' := fun x => show |a * x| = |x| by rw [map_mul, abs_coe_circle, one_mul] }
   map_one' := LinearIsometryEquiv.ext <| one_smul _
-  map_mul' _ _ := LinearIsometryEquiv.ext <| mul_smul _ _
+  map_mul' _ _ := LinearIsometryEquiv.ext <| hMul_smul _ _
 #align rotation rotation
 -/
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 François Sunatori. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: François Sunatori
-
-! This file was ported from Lean 3 source module analysis.complex.isometry
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Complex.Circle
 import Mathbin.LinearAlgebra.Determinant
 import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
 
+#align_import analysis.complex.isometry from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
 /-!
 # Isometries of the Complex Plane
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -197,7 +197,7 @@ theorem toMatrix_rotation (a : circle) :
     LinearMap.toMatrix basisOneI basisOneI (rotation a).toLinearEquiv =
       Matrix.planeConformalMatrix (re a) (im a) (by simp [pow_two, ← norm_sq_apply]) :=
   by
-  ext (i j)
+  ext i j
   simp [LinearMap.toMatrix_apply]
   fin_cases i <;> fin_cases j <;> simp
 #align to_matrix_rotation toMatrix_rotation

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

@@ -40,9 +40,9 @@ open Complex
 
 open scoped ComplexConjugate
 
--- mathport name: complex.abs
 local notation "|" x "|" => Complex.abs x
 
+#print rotation /-
 /-- An element of the unit circle defines a `linear_isometry_equiv` from `ℂ` to itself, by
 rotation. -/
 def rotation : circle →* ℂ ≃ₗᵢ[ℝ] ℂ
@@ -53,22 +53,30 @@ def rotation : circle →* ℂ ≃ₗᵢ[ℝ] ℂ
   map_one' := LinearIsometryEquiv.ext <| one_smul _
   map_mul' _ _ := LinearIsometryEquiv.ext <| mul_smul _ _
 #align rotation rotation
+-/
 
+#print rotation_apply /-
 @[simp]
 theorem rotation_apply (a : circle) (z : ℂ) : rotation a z = a * z :=
   rfl
 #align rotation_apply rotation_apply
+-/
 
+#print rotation_symm /-
 @[simp]
 theorem rotation_symm (a : circle) : (rotation a).symm = rotation a⁻¹ :=
   LinearIsometryEquiv.ext fun x => rfl
 #align rotation_symm rotation_symm
+-/
 
+#print rotation_trans /-
 @[simp]
 theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotation (b * a) := by
   ext1; simp
 #align rotation_trans rotation_trans
+-/
 
+#print rotation_ne_conjLie /-
 theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   by
   intro h
@@ -78,29 +86,39 @@ theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   rw [rotation_apply, conj_I, ← neg_one_mul, mul_left_inj' I_ne_zero, h1, eq_neg_self_iff] at hI 
   exact one_ne_zero hI
 #align rotation_ne_conj_lie rotation_ne_conjLie
+-/
 
+#print rotationOf /-
 /-- Takes an element of `ℂ ≃ₗᵢ[ℝ] ℂ` and checks if it is a rotation, returns an element of the
 unit circle. -/
 @[simps]
 def rotationOf (e : ℂ ≃ₗᵢ[ℝ] ℂ) : circle :=
   ⟨e 1 / Complex.abs (e 1), by simp⟩
 #align rotation_of rotationOf
+-/
 
+#print rotationOf_rotation /-
 @[simp]
 theorem rotationOf_rotation (a : circle) : rotationOf (rotation a) = a :=
   Subtype.ext <| by simp
 #align rotation_of_rotation rotationOf_rotation
+-/
 
+#print rotation_injective /-
 theorem rotation_injective : Function.Injective rotation :=
   Function.LeftInverse.injective rotationOf_rotation
 #align rotation_injective rotation_injective
+-/
 
+#print LinearIsometry.re_apply_eq_re_of_add_conj_eq /-
 theorem LinearIsometry.re_apply_eq_re_of_add_conj_eq (f : ℂ →ₗᵢ[ℝ] ℂ)
     (h₃ : ∀ z, z + conj z = f z + conj (f z)) (z : ℂ) : (f z).re = z.re := by
   simpa [ext_iff, add_re, add_im, conj_re, conj_im, ← two_mul,
     show (2 : ℝ) ≠ 0 by simp [two_ne_zero]] using (h₃ z).symm
 #align linear_isometry.re_apply_eq_re_of_add_conj_eq LinearIsometry.re_apply_eq_re_of_add_conj_eq
+-/
 
+#print LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re /-
 theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ}
     (h₂ : ∀ z, (f z).re = z.re) (z : ℂ) : (f z).im = z.im ∨ (f z).im = -z.im :=
   by
@@ -109,7 +127,9 @@ theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗ
   rwa [Real.sqrt_inj (norm_sq_nonneg _) (norm_sq_nonneg _), norm_sq_apply (f z), norm_sq_apply z,
     h₂, add_left_cancel_iff, mul_self_eq_mul_self_iff] at h₁ 
 #align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re
+-/
 
+#print LinearIsometry.im_apply_eq_im /-
 theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) :
     z + conj z = f z + conj (f z) :=
   by
@@ -125,14 +145,18 @@ theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
   simp only [add_sub, sub_left_inj] at this 
   rw [add_comm, ← this, add_comm]
 #align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_im
+-/
 
+#print LinearIsometry.re_apply_eq_re /-
 theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) : (f z).re = z.re :=
   by
   apply LinearIsometry.re_apply_eq_re_of_add_conj_eq
   intro z
   apply LinearIsometry.im_apply_eq_im h
 #align linear_isometry.re_apply_eq_re LinearIsometry.re_apply_eq_re
+-/
 
+#print linear_isometry_complex_aux /-
 theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
     f = LinearIsometryEquiv.refl ℝ ℂ ∨ f = conjLie :=
   by
@@ -151,7 +175,9 @@ theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
       intro i
       fin_cases i <;> simp [h, h']
 #align linear_isometry_complex_aux linear_isometry_complex_aux
+-/
 
+#print linear_isometry_complex /-
 theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
     ∃ a : circle, f = rotation a ∨ f = conjLie.trans (rotation a) :=
   by
@@ -162,7 +188,9 @@ theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
   · simpa using eq_mul_of_inv_mul_eq h₁
   · exact eq_mul_of_inv_mul_eq h₂
 #align linear_isometry_complex linear_isometry_complex
+-/
 
+#print toMatrix_rotation /-
 /-- The matrix representation of `rotation a` is equal to the conformal matrix
 `!![re a, -im a; im a, re a]`. -/
 theorem toMatrix_rotation (a : circle) :
@@ -173,7 +201,9 @@ theorem toMatrix_rotation (a : circle) :
   simp [LinearMap.toMatrix_apply]
   fin_cases i <;> fin_cases j <;> simp
 #align to_matrix_rotation toMatrix_rotation
+-/
 
+#print det_rotation /-
 /-- The determinant of `rotation` (as a linear map) is equal to `1`. -/
 @[simp]
 theorem det_rotation (a : circle) : ((rotation a).toLinearEquiv : ℂ →ₗ[ℝ] ℂ).det = 1 :=
@@ -181,10 +211,13 @@ theorem det_rotation (a : circle) : ((rotation a).toLinearEquiv : ℂ →ₗ[ℝ
   rw [← LinearMap.det_toMatrix basis_one_I, toMatrix_rotation, Matrix.det_fin_two]
   simp [← norm_sq_apply]
 #align det_rotation det_rotation
+-/
 
+#print linearEquiv_det_rotation /-
 /-- The determinant of `rotation` (as a linear equiv) is equal to `1`. -/
 @[simp]
 theorem linearEquiv_det_rotation (a : circle) : (rotation a).toLinearEquiv.det = 1 := by
   rw [← Units.eq_iff, LinearEquiv.coe_det, det_rotation, Units.val_one]
 #align linear_equiv_det_rotation linearEquiv_det_rotation
+-/
 

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

@@ -114,7 +114,7 @@ theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
     z + conj z = f z + conj (f z) :=
   by
   have : ‖f z - 1‖ = ‖z - 1‖ := by rw [← f.norm_map (z - 1), f.map_sub, h]
-  apply_fun fun x => x ^ 2  at this 
+  apply_fun fun x => x ^ 2 at this 
   simp only [norm_eq_abs, ← norm_sq_eq_abs] at this 
   rw [← of_real_inj, ← mul_conj, ← mul_conj] at this 
   rw [RingHom.map_sub, RingHom.map_sub] at this 

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

@@ -74,8 +74,8 @@ theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   intro h
   have h1 : rotation a 1 = conj 1 := LinearIsometryEquiv.congr_fun h 1
   have hI : rotation a I = conj I := LinearIsometryEquiv.congr_fun h I
-  rw [rotation_apply, RingHom.map_one, mul_one] at h1
-  rw [rotation_apply, conj_I, ← neg_one_mul, mul_left_inj' I_ne_zero, h1, eq_neg_self_iff] at hI
+  rw [rotation_apply, RingHom.map_one, mul_one] at h1 
+  rw [rotation_apply, conj_I, ← neg_one_mul, mul_left_inj' I_ne_zero, h1, eq_neg_self_iff] at hI 
   exact one_ne_zero hI
 #align rotation_ne_conj_lie rotation_ne_conjLie
 
@@ -105,24 +105,24 @@ theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗ
     (h₂ : ∀ z, (f z).re = z.re) (z : ℂ) : (f z).im = z.im ∨ (f z).im = -z.im :=
   by
   have h₁ := f.norm_map z
-  simp only [Complex.abs_def, norm_eq_abs] at h₁
+  simp only [Complex.abs_def, norm_eq_abs] at h₁ 
   rwa [Real.sqrt_inj (norm_sq_nonneg _) (norm_sq_nonneg _), norm_sq_apply (f z), norm_sq_apply z,
-    h₂, add_left_cancel_iff, mul_self_eq_mul_self_iff] at h₁
+    h₂, add_left_cancel_iff, mul_self_eq_mul_self_iff] at h₁ 
 #align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re
 
 theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) :
     z + conj z = f z + conj (f z) :=
   by
   have : ‖f z - 1‖ = ‖z - 1‖ := by rw [← f.norm_map (z - 1), f.map_sub, h]
-  apply_fun fun x => x ^ 2  at this
-  simp only [norm_eq_abs, ← norm_sq_eq_abs] at this
-  rw [← of_real_inj, ← mul_conj, ← mul_conj] at this
-  rw [RingHom.map_sub, RingHom.map_sub] at this
-  simp only [sub_mul, mul_sub, one_mul, mul_one] at this
-  rw [mul_conj, norm_sq_eq_abs, ← norm_eq_abs, LinearIsometry.norm_map] at this
-  rw [mul_conj, norm_sq_eq_abs, ← norm_eq_abs] at this
-  simp only [sub_sub, sub_right_inj, mul_one, of_real_pow, RingHom.map_one, norm_eq_abs] at this
-  simp only [add_sub, sub_left_inj] at this
+  apply_fun fun x => x ^ 2  at this 
+  simp only [norm_eq_abs, ← norm_sq_eq_abs] at this 
+  rw [← of_real_inj, ← mul_conj, ← mul_conj] at this 
+  rw [RingHom.map_sub, RingHom.map_sub] at this 
+  simp only [sub_mul, mul_sub, one_mul, mul_one] at this 
+  rw [mul_conj, norm_sq_eq_abs, ← norm_eq_abs, LinearIsometry.norm_map] at this 
+  rw [mul_conj, norm_sq_eq_abs, ← norm_eq_abs] at this 
+  simp only [sub_sub, sub_right_inj, mul_one, of_real_pow, RingHom.map_one, norm_eq_abs] at this 
+  simp only [add_sub, sub_left_inj] at this 
   rw [add_comm, ← this, add_comm]
 #align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_im
 

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

@@ -38,7 +38,7 @@ noncomputable section
 
 open Complex
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 -- mathport name: complex.abs
 local notation "|" x "|" => Complex.abs x

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

@@ -43,9 +43,6 @@ open ComplexConjugate
 -- mathport name: complex.abs
 local notation "|" x "|" => Complex.abs x
 
-/- warning: rotation -> rotation is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rotation rotationₓ'. -/
 /-- An element of the unit circle defines a `linear_isometry_equiv` from `ℂ` to itself, by
 rotation. -/
 def rotation : circle →* ℂ ≃ₗᵢ[ℝ] ℂ
@@ -57,33 +54,21 @@ def rotation : circle →* ℂ ≃ₗᵢ[ℝ] ℂ
   map_mul' _ _ := LinearIsometryEquiv.ext <| mul_smul _ _
 #align rotation rotation
 
-/- warning: rotation_apply -> rotation_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rotation_apply rotation_applyₓ'. -/
 @[simp]
 theorem rotation_apply (a : circle) (z : ℂ) : rotation a z = a * z :=
   rfl
 #align rotation_apply rotation_apply
 
-/- warning: rotation_symm -> rotation_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rotation_symm rotation_symmₓ'. -/
 @[simp]
 theorem rotation_symm (a : circle) : (rotation a).symm = rotation a⁻¹ :=
   LinearIsometryEquiv.ext fun x => rfl
 #align rotation_symm rotation_symm
 
-/- warning: rotation_trans -> rotation_trans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rotation_trans rotation_transₓ'. -/
 @[simp]
 theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotation (b * a) := by
   ext1; simp
 #align rotation_trans rotation_trans
 
-/- warning: rotation_ne_conj_lie -> rotation_ne_conjLie is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rotation_ne_conj_lie rotation_ne_conjLieₓ'. -/
 theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   by
   intro h
@@ -94,12 +79,6 @@ theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   exact one_ne_zero hI
 #align rotation_ne_conj_lie rotation_ne_conjLie
 
-/- warning: rotation_of -> rotationOf is a dubious translation:
-lean 3 declaration is
-  (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)
-but is expected to have type
-  (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) -> (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle))
-Case conversion may be inaccurate. Consider using '#align rotation_of rotationOfₓ'. -/
 /-- Takes an element of `ℂ ≃ₗᵢ[ℝ] ℂ` and checks if it is a rotation, returns an element of the
 unit circle. -/
 @[simps]
@@ -107,33 +86,21 @@ def rotationOf (e : ℂ ≃ₗᵢ[ℝ] ℂ) : circle :=
   ⟨e 1 / Complex.abs (e 1), by simp⟩
 #align rotation_of rotationOf
 
-/- warning: rotation_of_rotation -> rotationOf_rotation is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rotation_of_rotation rotationOf_rotationₓ'. -/
 @[simp]
 theorem rotationOf_rotation (a : circle) : rotationOf (rotation a) = a :=
   Subtype.ext <| by simp
 #align rotation_of_rotation rotationOf_rotation
 
-/- warning: rotation_injective -> rotation_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rotation_injective rotation_injectiveₓ'. -/
 theorem rotation_injective : Function.Injective rotation :=
   Function.LeftInverse.injective rotationOf_rotation
 #align rotation_injective rotation_injective
 
-/- warning: linear_isometry.re_apply_eq_re_of_add_conj_eq -> LinearIsometry.re_apply_eq_re_of_add_conj_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_isometry.re_apply_eq_re_of_add_conj_eq LinearIsometry.re_apply_eq_re_of_add_conj_eqₓ'. -/
 theorem LinearIsometry.re_apply_eq_re_of_add_conj_eq (f : ℂ →ₗᵢ[ℝ] ℂ)
     (h₃ : ∀ z, z + conj z = f z + conj (f z)) (z : ℂ) : (f z).re = z.re := by
   simpa [ext_iff, add_re, add_im, conj_re, conj_im, ← two_mul,
     show (2 : ℝ) ≠ 0 by simp [two_ne_zero]] using (h₃ z).symm
 #align linear_isometry.re_apply_eq_re_of_add_conj_eq LinearIsometry.re_apply_eq_re_of_add_conj_eq
 
-/- warning: linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re -> LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_reₓ'. -/
 theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ}
     (h₂ : ∀ z, (f z).re = z.re) (z : ℂ) : (f z).im = z.im ∨ (f z).im = -z.im :=
   by
@@ -143,9 +110,6 @@ theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗ
     h₂, add_left_cancel_iff, mul_self_eq_mul_self_iff] at h₁
 #align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re
 
-/- warning: linear_isometry.im_apply_eq_im -> LinearIsometry.im_apply_eq_im is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_imₓ'. -/
 theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) :
     z + conj z = f z + conj (f z) :=
   by
@@ -162,9 +126,6 @@ theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
   rw [add_comm, ← this, add_comm]
 #align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_im
 
-/- warning: linear_isometry.re_apply_eq_re -> LinearIsometry.re_apply_eq_re is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_isometry.re_apply_eq_re LinearIsometry.re_apply_eq_reₓ'. -/
 theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) : (f z).re = z.re :=
   by
   apply LinearIsometry.re_apply_eq_re_of_add_conj_eq
@@ -172,9 +133,6 @@ theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
   apply LinearIsometry.im_apply_eq_im h
 #align linear_isometry.re_apply_eq_re LinearIsometry.re_apply_eq_re
 
-/- warning: linear_isometry_complex_aux -> linear_isometry_complex_aux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_isometry_complex_aux linear_isometry_complex_auxₓ'. -/
 theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
     f = LinearIsometryEquiv.refl ℝ ℂ ∨ f = conjLie :=
   by
@@ -194,9 +152,6 @@ theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
       fin_cases i <;> simp [h, h']
 #align linear_isometry_complex_aux linear_isometry_complex_aux
 
-/- warning: linear_isometry_complex -> linear_isometry_complex is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_isometry_complex linear_isometry_complexₓ'. -/
 theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
     ∃ a : circle, f = rotation a ∨ f = conjLie.trans (rotation a) :=
   by
@@ -208,9 +163,6 @@ theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
   · exact eq_mul_of_inv_mul_eq h₂
 #align linear_isometry_complex linear_isometry_complex
 
-/- warning: to_matrix_rotation -> toMatrix_rotation is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align to_matrix_rotation toMatrix_rotationₓ'. -/
 /-- The matrix representation of `rotation a` is equal to the conformal matrix
 `!![re a, -im a; im a, re a]`. -/
 theorem toMatrix_rotation (a : circle) :
@@ -222,9 +174,6 @@ theorem toMatrix_rotation (a : circle) :
   fin_cases i <;> fin_cases j <;> simp
 #align to_matrix_rotation toMatrix_rotation
 
-/- warning: det_rotation -> det_rotation is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align det_rotation det_rotationₓ'. -/
 /-- The determinant of `rotation` (as a linear map) is equal to `1`. -/
 @[simp]
 theorem det_rotation (a : circle) : ((rotation a).toLinearEquiv : ℂ →ₗ[ℝ] ℂ).det = 1 :=
@@ -233,9 +182,6 @@ theorem det_rotation (a : circle) : ((rotation a).toLinearEquiv : ℂ →ₗ[ℝ
   simp [← norm_sq_apply]
 #align det_rotation det_rotation
 
-/- warning: linear_equiv_det_rotation -> linearEquiv_det_rotation is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_equiv_det_rotation linearEquiv_det_rotationₓ'. -/
 /-- The determinant of `rotation` (as a linear equiv) is equal to `1`. -/
 @[simp]
 theorem linearEquiv_det_rotation (a : circle) : (rotation a).toLinearEquiv.det = 1 := by

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

@@ -77,10 +77,8 @@ theorem rotation_symm (a : circle) : (rotation a).symm = rotation a⁻¹ :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align rotation_trans rotation_transₓ'. -/
 @[simp]
-theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotation (b * a) :=
-  by
-  ext1
-  simp
+theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotation (b * a) := by
+  ext1; simp
 #align rotation_trans rotation_trans
 
 /- warning: rotation_ne_conj_lie -> rotation_ne_conjLie is a dubious translation:
@@ -188,8 +186,7 @@ theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
     · rw [← I_re]
       exact @LinearIsometry.re_apply_eq_re f.to_linear_isometry h I
     · apply @LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re f.to_linear_isometry
-      intro z
-      rw [@LinearIsometry.re_apply_eq_re f.to_linear_isometry h]
+      intro z; rw [@LinearIsometry.re_apply_eq_re f.to_linear_isometry h]
   refine' h0.imp (fun h' : f I = I => _) fun h' : f I = -I => _ <;>
     · apply LinearIsometryEquiv.toLinearEquiv_injective
       apply complex.basis_one_I.ext'

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

@@ -44,10 +44,7 @@ open ComplexConjugate
 local notation "|" x "|" => Complex.abs x
 
 /- warning: rotation -> rotation is a dubious translation:
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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real 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Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align rotation rotationₓ'. -/
 /-- An element of the unit circle defines a `linear_isometry_equiv` from `ℂ` to itself, by
 rotation. -/
@@ -61,10 +58,7 @@ def rotation : circle →* ℂ ≃ₗᵢ[ℝ] ℂ
 #align rotation rotation
 
 /- warning: rotation_apply -> rotation_apply is a dubious translation:
-lean 3 declaration is
-  forall (a : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) 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(NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a) z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) a) z)
-but is expected to have type
-  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) a) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) a) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) 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(RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex 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: Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} 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Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) a) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{0, 0, 0, 0, 0} Real Real Complex Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) a) 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} 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(Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real 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Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) (MonoidHom.monoidHomClass.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex 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(Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation a) z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) a) z)
+<too large>
 Case conversion may be inaccurate. Consider using '#align rotation_apply rotation_applyₓ'. -/
 @[simp]
 theorem rotation_apply (a : circle) (z : ℂ) : rotation a z = a * z :=
@@ -72,10 +66,7 @@ theorem rotation_apply (a : circle) (z : ℂ) : rotation a z = a * z :=
 #align rotation_apply rotation_apply
 
 /- warning: rotation_symm -> rotation_symm is a dubious translation:
-lean 3 declaration is
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(Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a)) (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation (Inv.inv.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (DivInvMonoid.toHasInv.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Group.toDivInvMonoid.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (CommGroup.toGroup.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) circle.commGroup))) a))
-but is expected to have type
-  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) 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Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation (Inv.inv.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (InvOneClass.toInv.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivInvOneMonoid.toInvOneClass.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivisionMonoid.toDivInvOneMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivisionCommMonoid.toDivisionMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (CommGroup.toDivisionCommMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) commGroup))))) a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align rotation_symm rotation_symmₓ'. -/
 @[simp]
 theorem rotation_symm (a : circle) : (rotation a).symm = rotation a⁻¹ :=
@@ -83,10 +74,7 @@ theorem rotation_symm (a : circle) : (rotation a).symm = rotation a⁻¹ :=
 #align rotation_symm rotation_symm
 
 /- warning: rotation_trans -> rotation_trans is a dubious translation:
-lean 3 declaration is
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Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real 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(Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} 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(NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a) (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex 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(Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex 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Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation b)) (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring 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-but is expected to have type
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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation (HMul.hMul.{0, 0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (instHMul.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Submonoid.mul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle)) b a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align rotation_trans rotation_transₓ'. -/
 @[simp]
 theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotation (b * a) :=
@@ -96,10 +84,7 @@ theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotati
 #align rotation_trans rotation_trans
 
 /- warning: rotation_ne_conj_lie -> rotation_ne_conjLie is a dubious translation:
-lean 3 declaration is
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(SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} 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(Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a) Complex.conjLie
-but is expected to have type
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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation a) Complex.conjLie
+<too large>
 Case conversion may be inaccurate. Consider using '#align rotation_ne_conj_lie rotation_ne_conjLieₓ'. -/
 theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   by
@@ -125,10 +110,7 @@ def rotationOf (e : ℂ ≃ₗᵢ[ℝ] ℂ) : circle :=
 #align rotation_of rotationOf
 
 /- warning: rotation_of_rotation -> rotationOf_rotation is a dubious translation:
-lean 3 declaration is
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(Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (rotationOf (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex 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(RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a)) a
-but is expected to have type
-  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (rotationOf (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (fun (_x : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex 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+<too large>
 Case conversion may be inaccurate. Consider using '#align rotation_of_rotation rotationOf_rotationₓ'. -/
 @[simp]
 theorem rotationOf_rotation (a : circle) : rotationOf (rotation a) = a :=
@@ -136,20 +118,14 @@ theorem rotationOf_rotation (a : circle) : rotationOf (rotation a) = a :=
 #align rotation_of_rotation rotationOf_rotation
 
 /- warning: rotation_injective -> rotation_injective is a dubious translation:
-lean 3 declaration is
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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation)
-but is expected to have type
-  Function.Injective.{1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex 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Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex 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(NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) 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Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation)
+<too large>
 Case conversion may be inaccurate. Consider using '#align rotation_injective rotation_injectiveₓ'. -/
 theorem rotation_injective : Function.Injective rotation :=
   Function.LeftInverse.injective rotationOf_rotation
 #align rotation_injective rotation_injective
 
 /- warning: linear_isometry.re_apply_eq_re_of_add_conj_eq -> LinearIsometry.re_apply_eq_re_of_add_conj_eq is a dubious translation:
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(Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (coeFn.{1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)))) -> (forall (z : Complex), Eq.{1} Real (Complex.re (FunLike.coe.{1, 1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex 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(NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (UniformSpace.toTopologicalSpace.{0} Complex 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(NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) 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Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)) (Complex.re z))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_isometry.re_apply_eq_re_of_add_conj_eq LinearIsometry.re_apply_eq_re_of_add_conj_eqₓ'. -/
 theorem LinearIsometry.re_apply_eq_re_of_add_conj_eq (f : ℂ →ₗᵢ[ℝ] ℂ)
     (h₃ : ∀ z, z + conj z = f z + conj (f z)) (z : ℂ) : (f z).re = z.re := by
@@ -158,10 +134,7 @@ theorem LinearIsometry.re_apply_eq_re_of_add_conj_eq (f : ℂ →ₗᵢ[ℝ] ℂ
 #align linear_isometry.re_apply_eq_re_of_add_conj_eq LinearIsometry.re_apply_eq_re_of_add_conj_eq
 
 /- warning: linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re -> LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_reₓ'. -/
 theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ}
     (h₂ : ∀ z, (f z).re = z.re) (z : ℂ) : (f z).im = z.im ∨ (f z).im = -z.im :=
@@ -173,10 +146,7 @@ theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗ
 #align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_imₓ'. -/
 theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) :
     z + conj z = f z + conj (f z) :=
@@ -195,10 +165,7 @@ theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
 #align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_im
 
 /- warning: linear_isometry.re_apply_eq_re -> LinearIsometry.re_apply_eq_re is a dubious translation:
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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)) (Complex.re z))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_isometry.re_apply_eq_re LinearIsometry.re_apply_eq_reₓ'. -/
 theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) : (f z).re = z.re :=
   by
@@ -208,10 +175,7 @@ theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
 #align linear_isometry.re_apply_eq_re LinearIsometry.re_apply_eq_re
 
 /- warning: linear_isometry_complex_aux -> linear_isometry_complex_aux is a dubious translation:
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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) f (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Complex.instOneComplex))) -> (Or (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) f (LinearIsometryEquiv.refl.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) f Complex.conjLie))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_isometry_complex_aux linear_isometry_complex_auxₓ'. -/
 theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
     f = LinearIsometryEquiv.refl ℝ ℂ ∨ f = conjLie :=
@@ -234,10 +198,7 @@ theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
 #align linear_isometry_complex_aux linear_isometry_complex_aux
 
 /- warning: linear_isometry_complex -> linear_isometry_complex is a dubious translation:
-lean 3 declaration is
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Exists.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (fun (a : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} 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(NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} 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(NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} 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(RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real 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circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a)) (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f (LinearIsometryEquiv.trans.{0, 0, 0, 0, 0, 0} Real Real Real Complex Complex Complex Real.semiring Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real 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) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomCompTriple.right_ids.{0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (RingHomCompTriple.right_ids.{0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) Complex.conjLie (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a))))
-but is expected to have type
-  forall (f : LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))), Exists.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (fun (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => Or (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex 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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_isometry_complex linear_isometry_complexₓ'. -/
 theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
     ∃ a : circle, f = rotation a ∨ f = conjLie.trans (rotation a) :=
@@ -251,10 +212,7 @@ theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
 #align linear_isometry_complex linear_isometry_complex
 
 /- warning: to_matrix_rotation -> toMatrix_rotation is a dubious translation:
-lean 3 declaration is
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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex 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(MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} 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(NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} 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Real.nontrivial))))) (propext (Not False) True not_false_iff))) trivial)))
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(NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) a)))) (normSq_eq_of_mem_circle a))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (Field.toSemifield.{0} Real Real.field))))))) (congrArg.{1, 1} Prop Prop (Eq.{1} Real (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (Field.toSemifield.{0} Real Real.field))))))) False Not (Mathlib.Algebra.NeZero._auxLemma.3.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (Field.toSemifield.{0} Real Real.field)))) Real.instOneReal Complex.instNeZeroRealInstZeroRealOfNatToOfNat1InstOneReal))) not_false_eq_true))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align to_matrix_rotation toMatrix_rotationₓ'. -/
 /-- The matrix representation of `rotation a` is equal to the conformal matrix
 `!![re a, -im a; im a, re a]`. -/
@@ -268,10 +226,7 @@ theorem toMatrix_rotation (a : circle) :
 #align to_matrix_rotation toMatrix_rotation
 
 /- warning: det_rotation -> det_rotation is a dubious translation:
-lean 3 declaration is
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(Module.End.ring.{0, 0} Real Complex (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) Complex.addCommGroup (Complex.module.{0} Real Real.semiring Real.module)))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))) => (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) -> Real) (MonoidHom.hasCoeToFun.{0, 0} (LinearMap.{0, 0, 0, 0} 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) (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))))) (LinearIsometryEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) 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(DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring 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(NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
-but is expected to have type
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Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation a)))) Real.instOneReal))
+<too large>
 Case conversion may be inaccurate. Consider using '#align det_rotation det_rotationₓ'. -/
 /-- The determinant of `rotation` (as a linear map) is equal to `1`. -/
 @[simp]
@@ -282,10 +237,7 @@ theorem det_rotation (a : circle) : ((rotation a).toLinearEquiv : ℂ →ₗ[ℝ
 #align det_rotation det_rotation
 
 /- warning: linear_equiv_det_rotation -> linearEquiv_det_rotation is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module))))) (Units.mulOneClass.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) => (LinearEquiv.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (LinearEquiv.det._proof_1.{0} Real Real.commRing) (LinearEquiv.det._proof_2.{0} Real Real.commRing) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) -> (Units.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (MonoidHom.hasCoeToFun.{0, 0} (LinearEquiv.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (LinearEquiv.det._proof_1.{0} Real Real.commRing) (LinearEquiv.det._proof_2.{0} Real Real.commRing) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Units.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing))) (Monoid.toMulOneClass.{0} (LinearEquiv.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (LinearEquiv.det._proof_1.{0} Real Real.commRing) (LinearEquiv.det._proof_2.{0} Real Real.commRing) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearEquiv.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (LinearEquiv.det._proof_1.{0} Real Real.commRing) (LinearEquiv.det._proof_2.{0} Real Real.commRing) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearEquiv.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (LinearEquiv.det._proof_1.{0} Real Real.commRing) (LinearEquiv.det._proof_2.{0} Real Real.commRing) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearEquiv.automorphismGroup.{0, 0} Real Complex (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module))))) (Units.mulOneClass.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (LinearEquiv.det.{0, 0} Real Real.commRing Complex Complex.addCommGroup (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} 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-but is expected to have type
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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation a))) (Units.instCommGroupUnitsToMonoid.{0} Real Real.instCommMonoidReal))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_equiv_det_rotation linearEquiv_det_rotationₓ'. -/
 /-- The determinant of `rotation` (as a linear equiv) is equal to `1`. -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: François Sunatori
 
 ! This file was ported from Lean 3 source module analysis.complex.isometry
-! leanprover-community/mathlib commit ae690b0c236e488a0043f6faa8ce3546e7f2f9c5
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
 /-!
 # Isometries of the Complex Plane
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The lemma `linear_isometry_complex` states the classification of isometries in the complex plane.
 Specifically, isometries with rotations but without translation.
 The proof involves:

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

@@ -40,6 +40,12 @@ open ComplexConjugate
 -- mathport name: complex.abs
 local notation "|" x "|" => Complex.abs x
 
+/- warning: rotation -> rotation is a dubious translation:
+lean 3 declaration is
+  MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) 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(LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))
+but is expected to have type
+  MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) 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Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))
+Case conversion may be inaccurate. Consider using '#align rotation rotationₓ'. -/
 /-- An element of the unit circle defines a `linear_isometry_equiv` from `ℂ` to itself, by
 rotation. -/
 def rotation : circle →* ℂ ≃ₗᵢ[ℝ] ℂ
@@ -51,16 +57,34 @@ def rotation : circle →* ℂ ≃ₗᵢ[ℝ] ℂ
   map_mul' _ _ := LinearIsometryEquiv.ext <| mul_smul _ _
 #align rotation rotation
 
+/- warning: rotation_apply -> rotation_apply is a dubious translation:
+lean 3 declaration is
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Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a) z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) a) z)
+but is expected to have type
+  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) a) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) a) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) a) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, 0, 0} Real Real Complex Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) a) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField 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Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) a) z)
+Case conversion may be inaccurate. Consider using '#align rotation_apply rotation_applyₓ'. -/
 @[simp]
 theorem rotation_apply (a : circle) (z : ℂ) : rotation a z = a * z :=
   rfl
 #align rotation_apply rotation_apply
 
+/- warning: rotation_symm -> rotation_symm is a dubious translation:
+lean 3 declaration is
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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) 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(NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation (Inv.inv.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (DivInvMonoid.toHasInv.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Group.toDivInvMonoid.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (CommGroup.toGroup.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) circle.commGroup))) a))
+but is expected to have type
+  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.symm.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real 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(NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivisionCommMonoid.toDivisionMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (CommGroup.toDivisionCommMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) commGroup))))) a))
+Case conversion may be inaccurate. Consider using '#align rotation_symm rotation_symmₓ'. -/
 @[simp]
 theorem rotation_symm (a : circle) : (rotation a).symm = rotation a⁻¹ :=
   LinearIsometryEquiv.ext fun x => rfl
 #align rotation_symm rotation_symm
 
+/- warning: rotation_trans -> rotation_trans is a dubious translation:
+lean 3 declaration is
+  forall (a : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (b : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} 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Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex 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(MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} 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(MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex 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Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation (HMul.hMul.{0, 0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (instHMul.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Submonoid.mul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle)) b a))
+but is expected to have type
+  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (b : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.trans.{0, 0, 0, 0, 0, 0} Real Real Real Complex Complex Complex Real.semiring Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real 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) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomCompTriple.ids.{0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (RingHomCompTriple.ids.{0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) (MonoidHom.monoidHomClass.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex 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(Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation (HMul.hMul.{0, 0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (instHMul.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Submonoid.mul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle)) b a))
+Case conversion may be inaccurate. Consider using '#align rotation_trans rotation_transₓ'. -/
 @[simp]
 theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotation (b * a) :=
   by
@@ -68,6 +92,12 @@ theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotati
   simp
 #align rotation_trans rotation_trans
 
+/- warning: rotation_ne_conj_lie -> rotation_ne_conjLie is a dubious translation:
+lean 3 declaration is
+  forall (a : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle), Ne.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a) Complex.conjLie
+but is expected to have type
+  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Ne.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) 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(NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation a) Complex.conjLie
+Case conversion may be inaccurate. Consider using '#align rotation_ne_conj_lie rotation_ne_conjLieₓ'. -/
 theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   by
   intro h
@@ -78,6 +108,12 @@ theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
   exact one_ne_zero hI
 #align rotation_ne_conj_lie rotation_ne_conjLie
 
+/- warning: rotation_of -> rotationOf is a dubious translation:
+lean 3 declaration is
+  (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)
+but is expected to have type
+  (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) -> (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle))
+Case conversion may be inaccurate. Consider using '#align rotation_of rotationOfₓ'. -/
 /-- Takes an element of `ℂ ≃ₗᵢ[ℝ] ℂ` and checks if it is a rotation, returns an element of the
 unit circle. -/
 @[simps]
@@ -85,21 +121,45 @@ def rotationOf (e : ℂ ≃ₗᵢ[ℝ] ℂ) : circle :=
   ⟨e 1 / Complex.abs (e 1), by simp⟩
 #align rotation_of rotationOf
 
+/- warning: rotation_of_rotation -> rotationOf_rotation is a dubious translation:
+lean 3 declaration is
+  forall (a : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (rotationOf (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a)) a
+but is expected to have type
+  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (rotationOf (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (fun (_x : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) _x) 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+Case conversion may be inaccurate. Consider using '#align rotation_of_rotation rotationOf_rotationₓ'. -/
 @[simp]
 theorem rotationOf_rotation (a : circle) : rotationOf (rotation a) = a :=
   Subtype.ext <| by simp
 #align rotation_of_rotation rotationOf_rotation
 
+/- warning: rotation_injective -> rotation_injective is a dubious translation:
+lean 3 declaration is
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(NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} 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(NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation)
+but is expected to have type
+  Function.Injective.{1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex 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+Case conversion may be inaccurate. Consider using '#align rotation_injective rotation_injectiveₓ'. -/
 theorem rotation_injective : Function.Injective rotation :=
   Function.LeftInverse.injective rotationOf_rotation
 #align rotation_injective rotation_injective
 
+/- warning: linear_isometry.re_apply_eq_re_of_add_conj_eq -> LinearIsometry.re_apply_eq_re_of_add_conj_eq is a dubious translation:
+lean 3 declaration is
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(LinearIsometry.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f z)))) -> (forall (z : Complex), Eq.{1} Real (Complex.re (coeFn.{1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) => Complex -> Complex) (LinearIsometry.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f z)) (Complex.re z))
+but is expected to have type
+  forall (f : LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))), (forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex (instHAdd.{0} Complex Complex.instAddComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) z) => (fun 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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) a) (ContinuousMapClass.toFunLike.{0, 0, 0} (LinearIsometry.{0, 0, 0, 0} Real 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)))) -> (forall (z : Complex), Eq.{1} Real (Complex.re (FunLike.coe.{1, 1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)) (Complex.re z))
+Case conversion may be inaccurate. Consider using '#align linear_isometry.re_apply_eq_re_of_add_conj_eq LinearIsometry.re_apply_eq_re_of_add_conj_eqₓ'. -/
 theorem LinearIsometry.re_apply_eq_re_of_add_conj_eq (f : ℂ →ₗᵢ[ℝ] ℂ)
     (h₃ : ∀ z, z + conj z = f z + conj (f z)) (z : ℂ) : (f z).re = z.re := by
   simpa [ext_iff, add_re, add_im, conj_re, conj_im, ← two_mul,
     show (2 : ℝ) ≠ 0 by simp [two_ne_zero]] using (h₃ z).symm
 #align linear_isometry.re_apply_eq_re_of_add_conj_eq LinearIsometry.re_apply_eq_re_of_add_conj_eq
 
+/- warning: linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re -> LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re is a dubious translation:
+lean 3 declaration is
+  forall {f : LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)}, (forall (z : Complex), Eq.{1} Real (Complex.re (coeFn.{1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (fun (_x : LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) => Complex -> Complex) (LinearIsometry.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f z)) (Complex.re z)) -> (forall (z : Complex), Or (Eq.{1} Real (Complex.im (coeFn.{1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (fun (_x : LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) => Complex -> Complex) (LinearIsometry.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f z)) (Complex.im z)) (Eq.{1} Real (Complex.im (coeFn.{1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (fun (_x : LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) => Complex -> Complex) (LinearIsometry.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))))
+but is expected to have type
+  forall {f : LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))}, (forall (z : Complex), Eq.{1} Real (Complex.re (FunLike.coe.{1, 1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex 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Complex Complex (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)) (Complex.re z)) -> (forall (z : Complex), Or (Eq.{1} Real (Complex.im (FunLike.coe.{1, 1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex 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Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))))
+Case conversion may be inaccurate. Consider using '#align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_reₓ'. -/
 theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ}
     (h₂ : ∀ z, (f z).re = z.re) (z : ℂ) : (f z).im = z.im ∨ (f z).im = -z.im :=
   by
@@ -109,6 +169,12 @@ theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗ
     h₂, add_left_cancel_iff, mul_self_eq_mul_self_iff] at h₁
 #align linear_isometry.im_apply_eq_im_or_neg_of_re_apply_eq_re LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re
 
+/- warning: linear_isometry.im_apply_eq_im -> LinearIsometry.im_apply_eq_im is a dubious translation:
+lean 3 declaration is
+  forall {f : LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)}, (Eq.{1} Complex (coeFn.{1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) 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+but is expected to have type
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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z))))
+Case conversion may be inaccurate. Consider using '#align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_imₓ'. -/
 theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) :
     z + conj z = f z + conj (f z) :=
   by
@@ -125,6 +191,12 @@ theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
   rw [add_comm, ← this, add_comm]
 #align linear_isometry.im_apply_eq_im LinearIsometry.im_apply_eq_im
 
+/- warning: linear_isometry.re_apply_eq_re -> LinearIsometry.re_apply_eq_re is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Complex.instOneComplex))) -> (forall (z : Complex), Eq.{1} Real (Complex.re (FunLike.coe.{1, 1, 1} (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (UniformSpace.toTopologicalSpace.{0} Complex 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometry.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))))) f z)) (Complex.re z))
+Case conversion may be inaccurate. Consider using '#align linear_isometry.re_apply_eq_re LinearIsometry.re_apply_eq_reₓ'. -/
 theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) : (f z).re = z.re :=
   by
   apply LinearIsometry.re_apply_eq_re_of_add_conj_eq
@@ -132,6 +204,12 @@ theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
   apply LinearIsometry.im_apply_eq_im h
 #align linear_isometry.re_apply_eq_re LinearIsometry.re_apply_eq_re
 
+/- warning: linear_isometry_complex_aux -> linear_isometry_complex_aux is a dubious translation:
+lean 3 declaration is
+  forall {f : LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)}, (Eq.{1} Complex (coeFn.{1, 1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (fun (_x : LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) => Complex -> Complex) (LinearIsometryEquiv.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) -> (Or (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f (LinearIsometryEquiv.refl.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module))) (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f Complex.conjLie))
+but is expected to have type
+  forall {f : LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))}, (Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (FunLike.coe.{1, 1, 1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{0, 0, 0, 0, 0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedAddCommGroup.toPseudoMetricSpace.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{0, 0, 0, 0, 0} Real Real Complex Complex (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex 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Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) f (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Complex) => Complex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Complex.instOneComplex))) -> (Or (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} 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Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) f (LinearIsometryEquiv.refl.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) f Complex.conjLie))
+Case conversion may be inaccurate. Consider using '#align linear_isometry_complex_aux linear_isometry_complex_auxₓ'. -/
 theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
     f = LinearIsometryEquiv.refl ℝ ℂ ∨ f = conjLie :=
   by
@@ -152,6 +230,12 @@ theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
       fin_cases i <;> simp [h, h']
 #align linear_isometry_complex_aux linear_isometry_complex_aux
 
+/- warning: linear_isometry_complex -> linear_isometry_complex is a dubious translation:
+lean 3 declaration is
+  forall (f : LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)), Exists.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (fun (a : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} 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Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} 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(RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real 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circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a)) (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) f (LinearIsometryEquiv.trans.{0, 0, 0, 0, 0, 0} Real Real Real Complex Complex Complex Real.semiring Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real 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) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomCompTriple.right_ids.{0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (RingHomCompTriple.right_ids.{0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) Complex.conjLie (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a))))
+but is expected to have type
+  forall (f : LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))), Exists.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (fun (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => Or (Eq.{1} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) f (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) 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(NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real 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Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation a))))
+Case conversion may be inaccurate. Consider using '#align linear_isometry_complex linear_isometry_complexₓ'. -/
 theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
     ∃ a : circle, f = rotation a ∨ f = conjLie.trans (rotation a) :=
   by
@@ -163,6 +247,12 @@ theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
   · exact eq_mul_of_inv_mul_eq h₂
 #align linear_isometry_complex linear_isometry_complex
 
+/- warning: to_matrix_rotation -> toMatrix_rotation is a dubious translation:
+lean 3 declaration is
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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex 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(Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) a)))) (normSq_eq_of_mem_circle a)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real Real.field)))))))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real Real.field)))))))))) (rfl.{1} Real (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real Real.field)))))))))))) (Ne.def.{1} Real (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real Real.field)))))))))))) ((fun (a : Prop) (a_1 : Prop) (e_1 : Eq.{1} Prop a a_1) => congr_arg.{1, 1} Prop Prop a a_1 Not e_1) (Eq.{1} Real (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real Real.field))))))))))) False (propext (Eq.{1} Real (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real Real.field))))))))))) False ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : NeZero.{0} α _inst_1 (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))] => iff_false_intro (Eq.{1} α (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2))) (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1)))) (one_ne_zero.{0} α _inst_1 _inst_2 _inst_3)) Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real Real.field))))))) Real.hasOne (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) Real.nontrivial))))) (propext (Not False) True not_false_iff))) trivial)))
+but is expected to have type
+  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{0, 0, 0, 0} Real Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) Complex Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) => Matrix.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) Real) (LinearEquiv.toLinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (LinearIsometryEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real 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+Case conversion may be inaccurate. Consider using '#align to_matrix_rotation toMatrix_rotationₓ'. -/
 /-- The matrix representation of `rotation a` is equal to the conformal matrix
 `!![re a, -im a; im a, re a]`. -/
 theorem toMatrix_rotation (a : circle) :
@@ -174,6 +264,12 @@ theorem toMatrix_rotation (a : circle) :
   fin_cases i <;> fin_cases j <;> simp
 #align to_matrix_rotation toMatrix_rotation
 
+/- warning: det_rotation -> det_rotation is a dubious translation:
+lean 3 declaration is
+  forall (a : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle), Eq.{1} Real (coeFn.{1, 1} (MonoidHom.{0, 0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) Real (MulZeroOneClass.toMulOneClass.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (NonAssocSemiring.toMulZeroOneClass.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (NonAssocRing.toNonAssocSemiring.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Ring.toNonAssocRing.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Module.End.ring.{0, 0} Real Complex (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) Complex.addCommGroup (Complex.module.{0} Real Real.semiring Real.module)))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))) (fun (_x : MonoidHom.{0, 0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) Real (MulZeroOneClass.toMulOneClass.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (NonAssocSemiring.toMulZeroOneClass.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (NonAssocRing.toNonAssocSemiring.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Ring.toNonAssocRing.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Module.End.ring.{0, 0} Real Complex (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) Complex.addCommGroup (Complex.module.{0} Real Real.semiring Real.module)))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))) => (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) -> Real) (MonoidHom.hasCoeToFun.{0, 0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) Real (MulZeroOneClass.toMulOneClass.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (NonAssocSemiring.toMulZeroOneClass.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (NonAssocRing.toNonAssocSemiring.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Ring.toNonAssocRing.{0} (LinearMap.{0, 0, 0, 0} Real Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Module.End.ring.{0, 0} Real Complex (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) Complex.addCommGroup (Complex.module.{0} Real Real.semiring Real.module)))))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))) (LinearMap.det.{0, 0} Complex Complex.addCommGroup Real Real.commRing (Complex.module.{0} Real Real.semiring Real.module)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (HasLiftT.mk.{1, 1} (LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (CoeTCₓ.coe.{1, 1} (LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (coeBase.{1, 1} (LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearEquiv.LinearMap.hasCoe.{0, 0, 0, 0} Real Real Complex Complex Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (AddCommGroup.toAddCommMonoid.{0} Complex (SeminormedAddCommGroup.toAddCommGroup.{0} Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) (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))))) (LinearIsometryEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{0, 0, 0, 0} Real Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} 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(Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) Real (MulZeroOneClass.toMulOneClass.{0} (LinearMap.{0, 0, 0, 0} Real Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex 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+Case conversion may be inaccurate. Consider using '#align det_rotation det_rotationₓ'. -/
 /-- The determinant of `rotation` (as a linear map) is equal to `1`. -/
 @[simp]
 theorem det_rotation (a : circle) : ((rotation a).toLinearEquiv : ℂ →ₗ[ℝ] ℂ).det = 1 :=
@@ -182,6 +278,12 @@ theorem det_rotation (a : circle) : ((rotation a).toLinearEquiv : ℂ →ₗ[ℝ
   simp [← norm_sq_apply]
 #align det_rotation det_rotation
 
+/- warning: linear_equiv_det_rotation -> linearEquiv_det_rotation is a dubious translation:
+lean 3 declaration is
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(Semiring.toNonAssocSemiring.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (LinearEquiv.det._proof_1.{0} Real Real.commRing) (LinearEquiv.det._proof_2.{0} Real Real.commRing) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearEquiv.automorphismGroup.{0, 0} Real Complex (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring Real.module))))) (Units.mulOneClass.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing)))) (LinearEquiv.det.{0, 0} Real Real.commRing Complex Complex.addCommGroup (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module) (coeFn.{1, 1} (MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} 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(RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring 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(NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) (fun (_x : MonoidHom.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) => (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) -> (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module))) (MonoidHom.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module) (Complex.module.{0} Real Real.semiring Real.module)) (LinearIsometryEquiv.group.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))) (Complex.module.{0} Real Real.semiring Real.module)))))) rotation a))) (OfNat.ofNat.{0} (Units.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing))) 1 (OfNat.mk.{0} (Units.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing))) 1 (One.one.{0} (Units.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing))) (MulOneClass.toHasOne.{0} (Units.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing))) (Units.mulOneClass.{0} Real (Ring.toMonoid.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))))
+but is expected to have type
+  forall (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{0, 0, 0, 0} Real Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)))) (RingHomInvPair.ids.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing))) (RingHomInvPair.ids.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) => Units.{0} Real (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing))))) (LinearIsometryEquiv.toLinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (FunLike.coe.{1, 1, 1} (MonoidHom.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Submonoid.toMulOneClass.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle) (Monoid.toMulOneClass.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (DivInvMonoid.toMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (fun (a : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (Group.toDivInvMonoid.{0} (LinearIsometryEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex Complex (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))) (LinearIsometryEquiv.instGroupLinearIsometryEquivIdToNonAssocSemiringIds.{0, 0} Real Complex Real.semiring (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Complex (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Complex (NormedRing.toNonUnitalNormedRing.{0} Complex (NormedCommRing.toNormedRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)))))))))) rotation a))) (Units.instCommGroupUnitsToMonoid.{0} Real Real.instCommMonoidReal))))))))
+Case conversion may be inaccurate. Consider using '#align linear_equiv_det_rotation linearEquiv_det_rotationₓ'. -/
 /-- The determinant of `rotation` (as a linear equiv) is equal to `1`. -/
 @[simp]
 theorem linearEquiv_det_rotation (a : circle) : (rotation a).toLinearEquiv.det = 1 := by

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

@@ -38,7 +38,7 @@ open Complex
 open ComplexConjugate
 
 -- mathport name: complex.abs
-local notation "|" x "|" => Complex.AbsTheory.Complex.abs x
+local notation "|" x "|" => Complex.abs x
 
 /-- An element of the unit circle defines a `linear_isometry_equiv` from `ℂ` to itself, by
 rotation. -/
@@ -82,7 +82,7 @@ theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
 unit circle. -/
 @[simps]
 def rotationOf (e : ℂ ≃ₗᵢ[ℝ] ℂ) : circle :=
-  ⟨e 1 / Complex.AbsTheory.Complex.abs (e 1), by simp⟩
+  ⟨e 1 / Complex.abs (e 1), by simp⟩
 #align rotation_of rotationOf
 
 @[simp]

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

@@ -38,7 +38,7 @@ open Complex
 open ComplexConjugate
 
 -- mathport name: complex.abs
-local notation "|" x "|" => Complex.abs x
+local notation "|" x "|" => Complex.AbsTheory.Complex.abs x
 
 /-- An element of the unit circle defines a `linear_isometry_equiv` from `ℂ` to itself, by
 rotation. -/
@@ -82,7 +82,7 @@ theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie :=
 unit circle. -/
 @[simps]
 def rotationOf (e : ℂ ≃ₗᵢ[ℝ] ℂ) : circle :=
-  ⟨e 1 / Complex.abs (e 1), by simp⟩
+  ⟨e 1 / Complex.AbsTheory.Complex.abs (e 1), by simp⟩
 #align rotation_of rotationOf
 
 @[simp]
@@ -137,7 +137,7 @@ theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
   by
   have h0 : f I = I ∨ f I = -I :=
     by
-    have : |f I| = 1 := by simpa using f.norm_map Complex.i
+    have : |f I| = 1 := by simpa using f.norm_map Complex.I
     simp only [ext_iff, ← and_or_left, neg_re, I_re, neg_im, neg_zero]
     constructor
     · rw [← I_re]

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

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.

@@ -62,14 +62,14 @@ theorem rotation_trans (a b : circle) : (rotation a).trans (rotation b) = rotati
   simp
 #align rotation_trans rotation_trans
 
-theorem rotation_ne_conjLie (a : circle) : rotation a ≠ conjLie := by
+theorem rotation_ne_conjLIE (a : circle) : rotation a ≠ conjLIE := by
   intro h
   have h1 : rotation a 1 = conj 1 := LinearIsometryEquiv.congr_fun h 1
   have hI : rotation a I = conj I := LinearIsometryEquiv.congr_fun h I
   rw [rotation_apply, RingHom.map_one, mul_one] at h1
   rw [rotation_apply, conj_I, ← neg_one_mul, mul_left_inj' I_ne_zero, h1, eq_neg_self_iff] at hI
   exact one_ne_zero hI
-#align rotation_ne_conj_lie rotation_ne_conjLie
+#align rotation_ne_conj_lie rotation_ne_conjLIE
 
 /-- Takes an element of `ℂ ≃ₗᵢ[ℝ] ℂ` and checks if it is a rotation, returns an element of the
 unit circle. -/
@@ -123,7 +123,7 @@ theorem LinearIsometry.re_apply_eq_re {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1)
 #align linear_isometry.re_apply_eq_re LinearIsometry.re_apply_eq_re
 
 theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
-    f = LinearIsometryEquiv.refl ℝ ℂ ∨ f = conjLie := by
+    f = LinearIsometryEquiv.refl ℝ ℂ ∨ f = conjLIE := by
   have h0 : f I = I ∨ f I = -I := by
     simp only [ext_iff, ← and_or_left, neg_re, I_re, neg_im, neg_zero]
     constructor
@@ -140,7 +140,7 @@ theorem linear_isometry_complex_aux {f : ℂ ≃ₗᵢ[ℝ] ℂ} (h : f 1 = 1) :
 #align linear_isometry_complex_aux linear_isometry_complex_aux
 
 theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
-    ∃ a : circle, f = rotation a ∨ f = conjLie.trans (rotation a) := by
+    ∃ a : circle, f = rotation a ∨ f = conjLIE.trans (rotation a) := by
   let a : circle := ⟨f 1, by rw [mem_circle_iff_abs, ← Complex.norm_eq_abs, f.norm_map, norm_one]⟩
   use a
   have : (f.trans (rotation a).symm) 1 = 1 := by simpa using rotation_apply a⁻¹ (f 1)

Removes nonterminal simps on lines looking like simp [...]

@@ -155,7 +155,10 @@ theorem toMatrix_rotation (a : circle) :
     LinearMap.toMatrix basisOneI basisOneI (rotation a).toLinearEquiv =
       Matrix.planeConformalMatrix (re a) (im a) (by simp [pow_two, ← normSq_apply]) := by
   ext i j
-  simp [LinearMap.toMatrix_apply]
+  simp only [LinearMap.toMatrix_apply, coe_basisOneI, LinearEquiv.coe_coe,
+    LinearIsometryEquiv.coe_toLinearEquiv, rotation_apply, coe_basisOneI_repr, mul_re, mul_im,
+    Matrix.val_planeConformalMatrix, Matrix.of_apply, Matrix.cons_val', Matrix.empty_val',
+    Matrix.cons_val_fin_one]
   fin_cases i <;> fin_cases j <;> simp
 #align to_matrix_rotation toMatrix_rotation
 

• 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) 2021 François Sunatori. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: François Sunatori
-
-! This file was ported from Lean 3 source module analysis.complex.isometry
-! leanprover-community/mathlib commit ae690b0c236e488a0043f6faa8ce3546e7f2f9c5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Complex.Circle
 import Mathlib.LinearAlgebra.Determinant
 import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup
 
+#align_import analysis.complex.isometry from "leanprover-community/mathlib"@"ae690b0c236e488a0043f6faa8ce3546e7f2f9c5"
+
 /-!
 # Isometries of the Complex Plane
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -107,7 +107,7 @@ theorem LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re {f : ℂ →ₗ
 theorem LinearIsometry.im_apply_eq_im {f : ℂ →ₗᵢ[ℝ] ℂ} (h : f 1 = 1) (z : ℂ) :
     z + conj z = f z + conj (f z) := by
   have : ‖f z - 1‖ = ‖z - 1‖ := by rw [← f.norm_map (z - 1), f.map_sub, h]
-  apply_fun fun x => x ^ 2  at this
+  apply_fun fun x => x ^ 2 at this
   simp only [norm_eq_abs, ← normSq_eq_abs] at this
   rw [← ofReal_inj, ← mul_conj, ← mul_conj] at this
   rw [RingHom.map_sub, RingHom.map_sub] at this

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -157,7 +157,7 @@ theorem linear_isometry_complex (f : ℂ ≃ₗᵢ[ℝ] ℂ) :
 theorem toMatrix_rotation (a : circle) :
     LinearMap.toMatrix basisOneI basisOneI (rotation a).toLinearEquiv =
       Matrix.planeConformalMatrix (re a) (im a) (by simp [pow_two, ← normSq_apply]) := by
-  ext (i j)
+  ext i j
   simp [LinearMap.toMatrix_apply]
   fin_cases i <;> fin_cases j <;> simp
 #align to_matrix_rotation toMatrix_rotation